Having links to the Muslim Brotherhood should be considered a "possible indicator of extremism" but the group will not be banned, David Cameron said.
A long-awaited and diplomatically sensitive review of the group found that parts of the Muslim Brotherhood had a "highly ambiguous relationship with violent extremism", the Prime Minister told MPs.
Although there would be no immediate ban on the group, Mr Cameron said the Government would keep it under review to see if it meets the legal test for proscription as a terrorist organisation.
The review was completed last summer amid calls from allies such as Saudi Arabia for the UK to impose a ban on the group, and ministers have been accused of sitting on the report to avoid upsetting key partners in the Middle East.
The Brotherhood played a leading role in Egypt's 2011 revolution. It is considered a terrorist organisation by several countries but has also taken part in democratic elections on a peaceful platform.
But Cairo has waged a sweeping crackdown on senior figures from the Islamist group since its leader Mohammed Morsi was ousted as president by the military in 2013.
In a written statement to MPs, Mr Cameron said: "The Muslim Brotherhood comprises both a transnational network, with links in the UK, and national organisations in and outside the Islamic world.
"The movement is deliberately opaque, and habitually secretive."
The Prime Minister said the Brotherhood characterises Western societies and liberal Muslims as "decadent and immoral" and "it can be seen primarily as a political project".
But he continued: "Parts of the Muslim Brotherhood have a highly ambiguous relationship with violent extremism. Both as an ideology and as a network it has been a rite of passage for some individuals and groups who have gone on to engage in violence and terrorism."
Although it has stated its opposition to al Qaida, it has "never credibly denounced" the terrorist group's use of the work of Sayyid Qutb, one of the Brotherhood's most important historic figures.
Mr Cameron added that "individuals closely associated with the Muslim Brotherhood in the UK have supported suicide bombing and other attacks in Israel by Hamas", an organisation whose military wing was banned in the UK in 2001.
He said: "Muslim Brotherhood–associated and influenced groups in the UK have at times had a significant influence on national organisations which have claimed to represent Muslim communities (and on that basis have had a dialogue with Government), charities and some mosques.
"But they have also sometimes characterised the UK as fundamentally hostile to Muslim faith and identity; and expressed support for terrorist attacks conducted by Hamas.
"Aspects of the Muslim Brotherhood's ideology and activities therefore run counter to British values of democracy, the rule of law, individual liberty, equality and the mutual respect and tolerance of different faiths and beliefs."
The Prime Minister said the review's findings "support the conclusion that membership of, association with, or influence by the Muslim Brotherhood should be considered as a possible indicator of extremism".
He continued: "We will therefore keep under review the views that are promoted and activities that are undertaken by Muslim Brotherhood associates in the UK, in Arabic as well as English.
"We will consider whether any action under the counter extremism strategy or as part of our wider work may be appropriate, including action in line with the new engagement policy the Government will develop to ensure central and local government does not inadvertently provide legitimacy or a platform for extremists. We will challenge extremists' poisonous narratives and promote positive alternatives that show vulnerable people that there are better ways to get on in life."
The Government will continue to refuse visas to Brotherhood-linked extremists, ensure charities linked to the group are not misused to finance it instead of their "lawful charitable purpose", and keep the organisation's legal status under review.