Tensions have been on a knife-edge since Sunday when the hermit state claimed to have detonated a massive hydrogen bomb.
The White House said on Wednesday the US President and British Prime Minister had spoken on the phone about the growing threat on the Korean Peninsula.
And Mr Trump is said to have made it clear that no option, including military action, is off the table.
In a statement, the White House said: “They agreed that this latest reckless act only strengthens the world’s determination to confront the growing North Korea threat.
It added: “President Trump reiterated that now is not the time to talk to North Korea, and made clear that all options remain open to defend the United States and its allies against North Korean aggression.
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“The two leaders resolved to continue working closely together on increasing diplomatic and economic pressure on North Korea, and to call on others to do the same.”
News of the conversation was released after Mr Trump revealed he had also spoken to China about what should be done to hit back at the regime.
But despite refusing to take military action off the table in talks with Mrs May, the US President said military action “is not a first choice” after speaking with North Korea’s ally China.
Mr Trump said: “President Xi would like to do something. We’ll see whether or not he can do it.
“But we will not be putting up with what’s happening in North Korea.
“I believe that President Xi agrees with me 100 per cent. We had a very, very frank and very strong phone call.”
Mr Trump has previously threatened Kim Jong-un’s regime with “fire and fury”.
And US Ambassador to the United Nations Nikki Haley said on Monday that the North Korean leader was “begging for war”.
She said: “Enough is enough. We have taken an incremental approach, and despite the best of intentions, it has not worked.”
But British Defence Secretary Sir Michael Fallon claimed the US wanted to “leave no stone unturned” to find a non-military solution to the crisis.
He said: “The United States is perfectly entitled to make all the preparations it needs to protect its people, its bases, its own homeland, and they are clearly doing that at the moment to make sure the president has all the options that he needs.
“But equally, Secretary Mattis and I and others across the administration are very clear that we have to absolutely exhaust every possible diplomatic avenue to get this situation under control now.
“That means working intensively in New York (at the UN) over the next few days to get a new resolution, it means looking at the existing sanctions and making sure they are properly enforced, it means looking at the European Union level at what sanctions can be applied there, and above all it means putting more pressure on China to deal with its neighbour.”
China is focused on solving the Korean Peninsula nuclear issue through talks and peaceful means, Chinese President Xi Jinping told Mr Trump.
The US and South Korea have asked the United Nations to consider tough new sanctions on North Korea after its nuclear test on Sunday that Pyongyang said was a advanced hydrogen bomb.
Washington and its allies have said there is a growing urgency for China, North Korea’s top trading partner, to apply more pressure on its already isolated neighbour to get it to back down on its nuclear weapons and missiles programmes.
China “unswervingly” works to realise denuclearisation on the Korean Peninsula and to safeguard the international nuclear non-proliferation system, Xi told Mr Trump, according to a statement from China’s Foreign Ministry.