"The relationship between the two Presidents is an extremely close one, and will hopefully lead to a peaceful resolution of the North Korea problem", the White House said. The world's first atomic bomb, used on 6 August 1945, killed 140,000 people in Hiroshima, with the bombing of Nagasaki killing 70,000 more just three days later.
"Trump and Kim must immediately wind down the war of rhetoric, as the German Chancellor Angela Merkel has demanded", he said.
"We can not play fast and loose with nuclear weapons and nuclear threats".
Trump also reiterated their mutual commitment to denuclearisation of the Korean Peninsula, it added.
He said: "Our government must not drag our country into any military action over the Korea crisis, including joint exercises".
Mr Corbyn said, while the United Kingdom should play a role with other nuclear-armed countries to mediate the impasse between the countries, the Government not to offer "blind loyalty" to the Trump administration.More news: French leader urges calm in North Korea crisis
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Although Article 5 of the North Atlantic Treaty states that an attack on one NATO member is an act of aggression against the entire military alliance, the application of this provision is limited only to attacks on member states' territories in North America, Europe and the Atlantic. "Kim Jong-un, the world always thought he was not a responsible leader".
Trump on North Korea - Military solutions are locked in place.
Britain, America's top European ally, could formally refuse Donald Trump's call for help in waging war against North Korea, so long as Kim Jong-un does not strike Hawaii or the USA mainland.
Trump's warning came after the North Korea threatened to fire ballistic missiles over Japan towards the US Pacific island of Guam.
"This man will not get away with what he is doing", the billionaire said.