Russia's foreign minister has likened the war of words between Donald Trump and Kim Jong-un to a kindergarten fight between children.
The North Korean leader earlier labelled Mr Trump "mentally deranged" and a "dotard" after Mr Trump threatened to destroy his country.
Mr Trump responded with a tweet calling Kim Jong-un "a madman" who "will be tested like never before!"
Moscow's Sergei Lavrov said a pause was needed, "to calm down the hotheads".
"Yes, it's unacceptable to silently watch North Korea's nuclear military adventures but it is also unacceptable to unleash war on the Korean Peninsula," he said.
Kim Jong Un of North Korea, who is obviously a madman who doesn't mind starving or killing his people, will be tested like never before!— Donald J. Trump (@realDonaldTrump) September 22, 2017
He called for a political process, which he said was a key part of the United Nations Security Council process.
"Together with China we'll continue to strive for a reasonable approach and not an emotional one like when children in a kindergarten start fighting and no-one can stop them," he said.
The North Korean leader had attacked Donald Trump days after his speech at the UN, in which the US president said he would "totally destroy" North Korea if the US was forced to defend itself or its allies.
He also mocked Kim Jong-un with a disparaging nickname, saying: "Rocket man is on a suicide mission."
But the North Korean leader said remarks by the "deranged" US president convinced him he is right to develop weapons for North Korea.
In an unprecedented personal statement, Mr Kim said Mr Trump would "pay dearly" for his speech, which he labelled "unprecedented rude nonsense".
He said Mr Trump had insulted his country in the eyes of the world, and threatened to "surely and definitely tame the mentally deranged US dotard with fire."
Experts say this is the first time a North Korean leader has made a direct address to an international audience - and it merits serious and thorough consideration.
China also urged a calming of the heated rhetoric on both sides, saying the issue was "complicated and sensitive".
"All relevant parties should exercise restraint instead of provoking each other," said Foreign Minister spokesman Lu Kang.
North Korea's nuclear weapons programme has demonstrated unprecedented progress this year. It recently conducted its sixth nuclear test and now claims it has miniaturised a nuclear warhead to fit on a long-range missile.
North Korean Foreign Minister Ri Yong-ho earlier warned that Pyongyang could test a hydrogen bomb in the Pacific Ocean in response to the US president's threat.
That would demonstrate North Korea's claimed thermonuclear capability as a credible threat.
But the risk of such a move would be very high. It is not certain that missile defence systems in the Pacific could intercept the missile, and the risk of accidentally striking Japan - over which recent tests have flown - could spark a serious conflict.
Earlier, Mr Kim's comments had prompted swift criticism from the Japanese government.
Chief Cabinet Secretary Yoshihide Suga said in a news conference on Friday: "North Korea's remarks and behaviour are provocative to regional and international security, and they are absolutely unacceptable."
Mr Trump on Thursday signed a new order boosting sanctions against North Korea, where the US treasury would target firms and financial institutions doing business with Pyongyang.
He said: "For much too long North Korea has been allowed to abuse the international financial system to facilitate funding for its nuclear weapons and missile programs."
The UN Security Council had approved new rounds of sanctions earlier this month aimed at starving North Korea of fuel and income, which were in response to Pyongyang's much-condemned sixth nuclear test on 3 September.