Philip Hammond has urged South Korea to be "bigger" than its northern adversary and resist blasting propaganda across their border with loudspeakers.
The Foreign Secretary said the North Koreans were baiting Seoul and its allies by claiming to have successfully tested their first hydrogen bomb.
Mr Hammond, who is in Tokyo for talks with the Japanese government, said the international community should do what is needed to bring North Korea into line through sanctions, in return for restraint by its southern neighbour.
He said there was understanding of why South Korea felt the need to respond to the supposed escalation in its neighbour's nuclear capability.
But he added: "We have to be bigger than the North Koreans ... We know responding in this way is simply rising to the bait North Korea is presenting to us."
The claims by North Korea that it conducted a hydrogen bomb test are the top priority for talks during Mr Hammond's visit.
He previously hailed Japan as Britain's "closest security partner in Asia" as he arrived in the capital for discussions on security.
Kim Jong-un's secretive state said it successfully tested a miniaturised hydrogen bomb, a move that would be a significant advancement of its nuclear armoury, but experts have cast doubt on the claims.
Mr Hammond will discuss global security challenges with Japanese foreign minister Fumio Kishida alongside Defence Secretary Michael Fallon and his opposite number Gen Nakatani.
The Foreign Secretary, who arrived in the country after visits to China and the Philippines, will also meet Prime Minister Shinzo Abe.
"The UK and Japan are close allies. We enjoy a strong, historic relationship, based on common values and support for democracy, the rule of law, human rights and open markets," Mr Hammond said earlier.
"The long-term security of both the UK and Japan depend on upholding a stable international system. We will continue to work closely together to contribute to global prosperity, peace and security.
"The world today is increasingly dangerous, complex and uncertain. We face growing threats from terrorism and extremism, a resurgence in state-based threats including nuclear proliferation, and an escalation in challenges to our cyber security and to the rules-based international order.
"It is more important than ever for the UK to work with allies like Japan to counter these threats.
"As a permanent member of the UN Security Council, the UK is continuing to play a central role on the issues that matter and is working with allies like Japan to safeguard national security, as well as building our prosperity overseas."