The requests came on the heels of declarations by the secretive state that real conflict was inevitable, because of "hostile" U.S. troop exercises with South Korea and U.N. sanctions imposed over the North's latest nuclear weapons test.
They also followed South Korean media reports that the North, under its 30-year-old leader Kim Jong-un, had moved two missiles to the country's east coast.
"The current question was not whether, but when a war would break out on the peninsula," because of the "increasing threat from the United States", China's state news agency, Xinhua, on Friday quoted the North's Foreign Ministry as saying.
It added that diplomatic missions should consider evacuation. North Korea would provide safe locations for diplomats in accordance with international conventions, Xinhua quoted the ministry as saying in a notification to embassies.
On Saturday morning, a South Korean government official expressed bewilderment at the North's appeals to diplomats.
"As North Korea has many reasons behind the latest threats, it's hard to define what is its real intention," said the official, who asked not to be identified. "But it might have intensified these threats to strengthen the regime internally or to respond to international community."
There was no sign of tension on Seoul's rainsoaked streets, with traffic operating normally and no extra police visible.
The South Korean media reports on Friday said North Korea had placed two of its intermediate-range missiles on mobile launchers and hidden them on the east coast, a move that could threaten Japan or U.S. Pacific bases.
The report could not be confirmed, but White House spokesman Jay Carney said that based on past behaviour, "we would not be surprised" to see Pyongyang conduct another missile test.
Britain said its embassy in Pyongyang had been told by the North Korean government it "would be unable to guarantee the safety of embassies and international organisations in the country in the event of conflict from April 10th".
"We believe they have taken this step as part of their continuing rhetoric that the U.S. poses a threat to them," Britain's Foreign Office said.
It said it had "no immediate plans" to evacuate its embassy and accused the North Korean government of raising tensions "through a series of public statements and other provocations."
A Polish spokesman said the warning was "an inappropriate element of building up the pressure and we obviously think that there is no risk from outside on North Korea."
The United States, which does not have diplomatic relations with North Korea and is served by Sweden as a "protecting power" in Pyongyang, echoed the British and the Poles.
"This is just an escalating series of rhetorical statements, and the question is, to what end?" said U.S. State Department spokeswoman Victoria Nuland.
Asked if the United States had received any instructions from the Swedes on the small number of U.S. aid workers or tourists who could be in North Korea, she said there was no indication Sweden would heed Pyongyang's warning.
Brazil's foreign minister said its ambassador could be moved to Dandong, a city across the Chinese border, though its embassy had an underground shelter and a power generator.
"We will evaluate exactly what the conditions are before we make a decision on his stay," Antonio Patriota told a news conference in Brasilia.
U.N. Secretary-General Ban Ki-moon "remains deeply concerned about escalating tensions on the Korean peninsula," but U.N. humanitarian workers remain active across North Korea for the time being, a spokesman said on Friday.
"U.N. staff in the DPRK (North Korea) remain engaged in their humanitarian and developmental work throughout the country," said U.N. spokesman Martin Nesirky. The United Nations has 36 international staff and 21 locally recruited personnel working in North Korea, the world body said.
Under the Vienna Convention that governs diplomatic missions, host governments are required to help get embassy staff out of the country in the event of conflict.
Russia's Foreign Ministry said North Korea had "proposed that the Russian side consider the evacuation of employees in the increasingly tense situation", according to a spokesman for its embassy in Pyongyang.
Moscow said it was "seriously studying" the request.
Kim Jong-un is the third member of his dynasty to rule North Korea. He took over in December 2011 after the death of his father, Kim Jong-il, who staged confrontations with South Korea and the United States throughout his 17-year rule.
In a fusillade of statements over the past month, North Korea has threatened to stage a nuclear strike on the United States, something it lacks the capacity to do, according to most experts, and has declared war on South Korea.
The threats against the United States are "probably all bluster", said Gary Samore, until recently the top nuclear proliferation expert on President Barack Obama's national security staff.
The North Koreans "are not suicidal. They know that any kind of direct attack (on the United States) would be end of their country," he added.
Speculation about missile movements centred on two types of weapon, neither of which is known to have been tested.
One is the so-called Musudan missile, which South Korea's Defence Ministry estimates has a range of up to 3,000 km (1,865 miles). The other is the KN-08, believed to be an intercontinental ballistic missile.
North Korea has always condemned the military exercises held by U.S. forces and their South Korean allies, but its reaction to this year's has reached a blistering pitch.
CASTRO WARNS AGAINST WAR
Former Cuban leader Fidel Castro, in an essay in Cuban state media, warned ally North Korea against war, describing the situation on the Korean Peninsula as "incredible and absurd" and "one of the gravest risks of nuclear war since the Crisis of October (Cuban Missile Crisis), 50 years ago.
The verbal assaults from Pyongyang have set financial markets in South Korea, Asia's fourth largest economy, on edge.
South Korean shares slid on Friday, with foreign investors selling their biggest daily volume in nearly 20 months, hurt after aggressive easing from the Bank of Japan sent the yen reeling, as well as by the tension over North Korea.