Former Defence Secretary Liam Fox has also called for heightened security at home to stop British-born jihadists returning to the UK from Iraq from carrying out terrorism.
In an article for the Sunday Telegraph he said there would be "catastrophic" security consequences if extremism is not defeated, and urged the Government to send British military assets to the region to assist any American-led attacks on Isis, saying the UK "should not rule out acting where we could provide specific help".
Fox suggested a majority of people would accept that an "idealogical battle" would necessitate the need for increased snooping powers for intelligence agencies.
He said: "There are those who say if we don't get involved, if we hunker down then we will be fine. There will be no backlash.
"That is utterly, utterly wrong because the jihadists don't hate us because of what we do. They hate us because of who we are. We can't change that.
"It is our values and our history that they detest more than anything else."
Meanwhile, a top counter-terrorism expert has said Britain will feel the repercussions of Syria and the rise of Islamic extremism within its own borders for "many years" to come.
Cressida Dick, the Metropolitan Police's assistant commissioner and head of specialist operations, warned that Britain would feel long-term consequences of the conflict.
She told the BBC it represented a terrorist threat to the UK, and that young British Muslims who have travelled to the war-torn country to fight might commit violence when they return.
Dick told BBC Radio 4's The World This Weekend: "I'm afraid I believe that we will be living with the consequences of Syria - from a terrorist point of view, let alone the world, geopolitical consequences - for many, many, many years to come."
Her warning came after footage emerged online apparently showing several young British jihadists in Syria in a recruitment video for the extremist militant group Islamic State in Iraq and Syria (Isis), in which they urge UK Muslims to join insurgents there and in Iraq.
Two have been identified as brothers from Cardiff - 20-year-old Nasser Muthana, and 17-year-old Aseel Muthana.
Two other men were arrested in March and April in the UK after they returned from Syria. The pair, aged 19 and 23 and both also from Cardiff, were held on suspicion of receiving terrorist training and attending a place used for terrorist training, but were later released without charge.
South Wales Police said in a statement: "We are increasingly concerned about the numbers of young people who have or are intending to travel to Syria to join the conflict.
"The advice is to avoid all travel to Syria - anyone who does travel is putting themselves in considerable danger. Travelling abroad for the purpose of engaging in terrorist related activity is an offence and we will seek to prosecute anyone engaged in this type of activity.
"The issue is not unique to Cardiff or Wales and is a priority for police and security services across the UK."
Police across the UK have made 65 Syria-related arrests over the last 18 months, including 40 in the first three months of this year alone.
Yesterday it emerged that around 500 Britons had travelled to Syria and Iraq - a higher estimate than the 400 claimed by Foreign Secretary William Hague.
Sir Peter Fahy, who leads on the Prevent counter-terrorism strategy for the Association of Chief Police Officers, said "huge amounts of material" was being taken down from the internet every week as part of the effort to stop people being radicalised.
Another terrorism expert warned that it is "inevitable" that jihadists returning from Syria and Iraq will pose a threat in Britain, saying that hundreds of radicalists may have already returned.
Richard Barrett, a former head of counter-terrorism at MI6, estimated that "possibly up to 300 people have come back to the UK" already, and warned that intelligence services faced an "impossible" task in trying to track them.
He told The Independent on Sunday: "If you imagine what it would cost to really look at 300 people in depth, clearly it would be completely impossible to do that, probably impossible even at a third of that number."
Mr Barrett said police and intelligence resources were stretched in terms of numbers and knowing where the returning jihadists are.
He said: "With this whole business in Syria, although there is no linear projection from foreign fighters to domestic terrorists, it's inevitable that a number will fall into this category."
Mr Barrett has co-authored a report, released this month, which concludes that more than 12,000 foreign fighters have gone to Syria since the war began, and that it is "likely to be an incubator for a new generation of terrorists".
Meanwhile the father of the Muthana brothers said his sons, both high achievers at school with good career prospects, must have been "brainwashed" and believes a network of radical jihadi recruiters must have paid for them to go.
Mr Muthana said that he and his wife were "devastated" when they found out from police in November that their eldest son Nasser had joined a terror cell in Syria. In February police informed them their second son, Aseel had obtained a second passport and travelled to Cyprus and was planning to join his brother.
Mr Muthana, 57, told the Sunday Telegraph: "Behind this are Islamic radicals, hiding behind the scenes, influencing the minds of young people. It is not members of the Yemeni community in Cardiff. Someone is persuading them, brainwashing them, helping them travel, arranging tickets."
Nasser was reported to have passed 14 GCSEs, was studying for his A-levels and had been offered places to study medicine at four universities before he became radicalised. His brother Aseel was an A-level student at Fitzalan High School in Cardiff and had dreams of becoming an English teacher.
Mr Muthana, who came to the UK in the 1970s from Yemen, told the newspaper: "I feel sick and devastated my son is caught up in this - they were brought up to love and respect my country Britain. Now I fear they may come back in coffins.
"I'm worried about their safety. But I am also worried about the evil messages Nasser is spreading in this vile video - I am concerned that other boys may follow him there."
The brothers were part of a wider terror network that included two friends arrested months ago after they returned from the Middle East, the newspaper reported.
Yesterday thousands of young British Muslim men rallied against radical Islam amid the concerns that British jihadists are fighting in Syria.
An estimated 5,000 Muslims gathered in Surrey to pledge loyalty to Britain in light of concerns over the popularity of Isis and the alleged involvement of Britons.
The three-day residential event, organised by the Ahmadiyya Muslim Youth Association (Amya), has brought together 5,000 young British Muslim men from England, Scotland and Wales, to foster bonds of brotherhood and affirm their pride in being British and Muslim.
Shadow justice secretary Sadiq Khan warned that radicalisation in prisons was a big problem and described the inadequacy of training for prison staff to deal with the issue as "shocking".
Mr Khan said mosques do a good job in educating young people and called on the Government to concentrate on the spaces it can govern, such as prisons.
He told Sky News's Murnaghan programme: "You speak to prison governors, as I do, prison officers, as I do - the inadequacy of the training is quite shocking.
"But also their inability to tackle this problem is a big issue and we should be doing much, much more.
"There's no point in politicians from this Government coming on with their heads in their hands, blaming parents or mosques - important roles that they have to play as well."
Earlier, he told the programme: "The mosques actually do a good job. Actually most mums and dads don't want their young sons, we've seen the father of the two sons in Cardiff, being radicalised.
"The problem is with the internet now, with social media, with Twitter.
"Our ability as parents or as governors of a mosque are less than they were and we've got to redouble our efforts to stop the source, these preachers of hate, getting into people's bedrooms.
"I think we've got to recognise that if you are a young person born and raised in this country and the first time somebody shows you a role model is a bearded man with a Kalashnikov in Afghanistan, or somebody doing bad things in Syria or Iraq, it's a problem."
Dick told BBC Radio 4's The World This Weekend it was "very difficult" to know who has travelled to Syria and Iraq and where they are.
She warned Britons against travelling to the conflicts, even for humanitarian reasons, saying it is likely they would get killed or caught up in a dangerous situation.
Dick told the programme: "My message to them is don't (travel), we'll do everything we can to stop you from travelling.
"Secondly, you are almost certainly going to be committing offences and find yourself in an incredibly dangerous position.
"Even if you think you are going for humanitarian purposes, you are extremely likely to get tangled up in something which will either end up killed, kidnapped, or perhaps engaged in fighting yourself, so don't travel."
Dick also stressed it was difficult to know exactly why people are radicalised and their motivation for wanting to carry out terrorist attacks.
She said the threat to Britain from people going abroad to fight could manifest itself in either an attack planned from a conflict zone, or by inspiring people who return from war to "take up arms".
Dick said: "This is a phenomenon we are used to. Terrorist groups in other countries may on occasion seek to launch an attack from there, for example to send people back in this instance, perhaps European foreign fighters.
"Or they may seek simply to encourage people to come back and self start, if you like - so choose their target, choose their time, choose their way of doing things.
"By their very nature, these groups, particularly in our internet age, inspire people in our country, and people who have perhaps returned from a theatre of war to do things and we've seen several international terrorist groups seeking to encourage people, including in this country, to get up and, for want of a better word, take arms and try to kill people here.
"This is a very real phenomenon, it's also one which is extremely hard to disentangle precise motivation - how people become radicalised, how people become inspired, how they learn what they want to do, and then how they decide what they want to do."
The mother of Reyaad Khan, from Cardiff, has appealed to her only son to come home after he appeared in a video, released by Isis calling Muslims to fight in Syria and Iraq.
In an interview with Sky News the woman, who was not identified, said she felt "absolutely shocked" when she saw the video.
"He is honest, always caring for his family, he always wanted to be there for them. He was one of the best boys a mother could ever want," she told Sky News.
"I think they are brainwashed into thinking they are going to help people. I don't know who it is but there is someone behind them keeping these young, innocent boys, brainwashing them into thinking they are going to help people. There is someone behind them, I don't know who."
The mother said the actions of her 20-year-old son had hugely impacted on her family.
"It is absolutely devastating. It has turned our lives upside down. I can't sleep or eat, I am very ill," she said.
In a direct appeal to her son, the woman sobbed as she said: "Reyaad, please come back home. I'm dying for you. You're my only son. Please come back Reyaad."
She also begged Isis: "Please send my son back home. He is my one and only son. I and my family need him back. Please just send my son back to me before I die and it is going to be too late for Reyaad, he's going to regret it for the rest of his life.
"Please send my son back to me and his family. We all need him."