US Secretary of State Rex Tillerson discussed the need to boost pressure on North Korea in talks with Prime Minister Theresa May in London on Thursday where the Iran nuclear deal was also raised.
The two discussed North Korea's "destabilising activities" and the importance of the international community coming together "to put pressure on the regime," May's spokesman said.
On the Iran nuclear deal, which is viewed sceptically in Washington, May was "underlining its importance in preventing Iran from procuring nuclear weapons," the spokesman said.
Tillerson's policy adviser Brian Hook said the Secretary of State "never misses an opportunity in bilateral, multilateral settings to raise North Korea and the need to increase pressure on North Korea".
Tillerson is also scheduled to meet with his British counterpart and a French foreign ministry official in London later on Thursday.
British Foreign Minister Boris Johnson reiterated Britain's commitment to tackle "the aggressive and illegal actions of the North Korean regime".
"The UK is at the heart of mobilising world opinion with the aim of achieving a diplomatic solution to the situation on the Korean peninsula," Johnson said in a statement ahead of the meeting.
On September 3, North Korea detonated its sixth and most powerful nuclear test to date, prompting the UN Security Council to implement new sanctions.
Although Britain and France backed the US demand for tougher sanctions, the final resolution was toned down to secure backing from China and Russia.
In another meeting, Tillerson will also discuss the situation in Libya, where two competing governments and dozens of militias have jousted for power followed the 2011 overthrow of longtime dictator Moamer Kadhafi.
The aim of the meeting -- attended by the UN envoy for Libya Ghassan Salamé and representatives from France, Italy, Egypt and the United Arab Emirates -- is to "discuss how to break the political deadlock in Libya," Britain's foreign ministry said.
The US hopes the trip will give "new energy and focus to mediation efforts led by the United Nations," Hook said.
"The big goal of this is to avoid a military solution," he added, warning that the lack of stability in the country "creates space for terrorists to plot attacks against the West".
In July, the UN-backed Government of National Accord headed by Fayez al-Sarraj and east Libyan strongman Khalifa Haftar committed to a ceasefire and holding elections as soon as possible.