By Tom Phillips, Shanghai and David Blair
Delivering another warning, North Korea also vowed to wage a “merciless sacred retaliatory war” if provoked by its enemies.
But the Foreign Office said there was no plan to change its travel advice, which currently does not warn Britons against visiting either South or North Korea. The British embassies in both countries also remain open.
A spokesman said the situation was kept “under continuous review”, but added: “We don't currently assess that we need to change the advice.”
The latest provocative statement from Kim Jong-un's regime follows the tightening of United Nations sanctions in retaliation for North Korea's third nuclear test in February.
Few experts believe that North Korea is genuinely plotting an attack on its southern neighbour. There has been no mass mobilisation of troops near the border, nor has the North's capital, Pyongyang, been placed on a war-footing. Any full-scale war would pit the North against the United States, guaranteeing its defeat.
Instead, the continuous verbal offensive could be an attempt to craft Mr Kim's domestic image as a powerful leader.
Tuesday's statement urged “all foreign institutions and enterprises and foreigners including tourists” in South Korea to “take measures for shelter and evacuation”. It added: “The situation on the Korean Peninsula is inching close to a thermo-nuclear war due to the evermore undisguised hostile actions of the United States and the South Korean puppet warmongers.”
Around 1.4 million foreigners live in South Korea. The country has the world's 12th biggest economy and some 100,000 Britons visit every year.
While Mr Kim may not intend to start a full-scale war, the danger is that a small incident could trigger an escalation. North Korea has moved two long-range Musudan missiles to its eastern coast, the location for previous test launches. If either weapon is fired - even for testing purposes - that would increase the tension still further.
Ban Ki-moon, the UN secretary general and a former foreign minister of South Korea, said the situation was “very dangerous”, adding: “A small incident caused by miscalculation or misjudgement may create an uncontrollable situation.”
South Korea downplayed its neighbour's latest outburst. “Fuelling tension has been a trademark tactic employed for decades by the North to deal with outside pressure against its bad behaviour and win concessions,” an official told Yonhap, the country's news agency.
President Park Geun-hye, South Korea's newly elected leader, called for an end to the “vicious cycle” of North Korea continually “creating crises” in order to extract concessions.
Last week, North Korea gave foreign embassies in Pyongyang until today to say whether they needed help with evacuating staff. So far, none are believed to have acted on this warning. All European Union missions remain open. Some tourists have continued to visit Pyongyang without encountering problems.
”I knew that when I arrived here it would probably be very different to the way it was being reported in the media,” Mark Fahey, an Australian tourist told Associated Press, the only western news outlet allowed a semi-permanent presence in Pyongyang.
Regional governments also view a pre-emptive North Korean strike as unlikely, but they are taking no chances. Japan said it had deployed PAC-3 missile interceptors around Tokyo.