The North's move comes amid threats to attack the United States and South Korean targets.
South Korea has reportedly deployed two warships with missile defence systems after the North was said to have moved a missile to its east coast.
Military officials told South Korean media that the two warships would be deployed on the east and west coasts.
"What Pyongyang is daily threatening is a fantasy. If they did any of it, this would be suicidal,” said a Korean military official.
Seoul has played down the North's missile move: It said the move may be for a test rather than a hostile act. For its part, the US said it would not be surprised if North Korea were to conduct a new missile test, with White House spokesman Jay Carney telling reporters Friday: "We have seen them launch missiles in the past."
British diplomats said yesterday that the North had asked them to respond by 10 April on what support the embassy would need in the event of any evacuation – and they were considering their moves.
"We are consulting international partners about these developments. No decisions have been taken, and we have no immediate plans to withdraw our Embassy,” said a Foreign and Commonwealth Office statement.
Russian Foreign Minister Sergei Lavrov said Moscow was "deeply concerned about the escalation of tension, which for now is verbal".
"We want to understand the reasons behind this offer. We were interested in finding out whether this was a decision taken by the North Korean leadership to evacuate embassies, or just an offer."
Anecdotal reports from Pyongyang suggest the mood there is calm, and many believe North Korea is deliberately trying to create a sense of crisis, says the BBC's Lucy Williamson in Seoul. One of the US targets named by Pyongyang was the Pacific Island of Guam, which hosts a US military base.
On Thursday, the US confirmed it would deploy a missile defence system to Guam in response to the threats.
South Korea's foreign minister told MPs on Thursday that the North had moved a missile to the east coast, which is the location for previous military tests.
Unconfirmed reports yesterday said the North had moved two missiles – thought to be mid-range Musudans, which are untested in flight but are thought to have the capacity to reach as far as Guam – and loaded them on to launchers.
Yonhap, the South Korean news agency, said that two warships equipped with Aegis defence systems would monitor the situation.