The Foreign Office has condemned "provocations" by the North Korean government but said it has "no immediate plans" to withdraw Britain's embassy from Pyongyang.
British officials were warned earlier that the authorities in North Korea's capital would be unable to guarantee their safety if war broke out after April 10.
The UK Government criticised Kim Jong Un's regime for ramping up tensions through a series of provocative moves over recent weeks and urged it to work "constructively" with the international community. It is now in discussions with other governments about the latest developments.
A Foreign and Commonwealth Office spokesman said on Friday: "Earlier today, the North Korean Ministry of Foreign Affairs informed a number of embassies of foreign countries in Pyongyang, including the British Embassy, and representatives of international organisations that they would be unable to guarantee the safety of embassies and international organisations present in the country in the event of conflict.
"They invited the embassies and organisations present at the meeting to inform them by April 10 what assistance they would require from the DPRK should they wish to be evacuated from DPRK or to be relocated elsewhere. We are consulting international partners about these developments. No decisions have been taken, and we have no immediate plans to withdraw our embassy.
"In recent weeks, the North Korean Government has raised tensions on the Korean peninsula and the wider region through a series of public statements and other provocations. We condemn this behaviour and urge the North Korean Government to work constructively with the international community, including over the presence of foreign embassies."
The Government has warned North Korea of its obligations under the international Vienna convention to protect diplomatic missions and claimed the move was an example of the "continuing rhetoric" against the United States.
On Thursday Prime Minister David Cameron said Kim Jong Un's regime possessed weapons which could threaten the UK. He warned: "If they are able to reach the whole of the United States they can reach Europe too, they can reach us too. That is a real concern."
The latest crisis in relations on the Korean peninsula follows anger in Pyongyang about sanctions against its nuclear programme and joint military drills involving US and South Korean forces.
North Korea's military on Thursday warned it had been authorised to attack the US, while South Korea's defence minister claimed its neighbour had moved a missile with "considerable range" to the east coast, potentially able to hit targets in the South or Japan. South Korea has reportedly deployed two warships with missile-defence systems in response.