US President Donald Trump said late on Tuesday he's received a letter from Volodymyr Zelensky agreeing to "come to the negotiating table" to strike a peace deal with Russia and also announced Russia is “ready for peace”.

"I appreciate that he sent this letter," Trump said as he addressed a joint session of Congress in Washington, BBC reported.

It came after Zelensky said in a social media post that he was ready to work under Trump's "strong leadership" to achieve a lasting peace.

The statements indicate a cooling of tensions between the leaders following their fiery meeting in the Oval Office last week.

In his address to Congress, Trump said he received an "important letter" from Zelensky on Tuesday, before reading what he said were excerpts from it.

Parts of what he read used precisely the same language as the statement posted by Zelensky earlier on Tuesday.

"The letter reads Ukraine is ready to come to the negotiating table as soon as possible to bring lasting peace closer. Nobody wants peace more than the Ukrainians," Trump said.

Continuing to read from what he said was Zelensky's letter, Trump said: "My team and I stand ready to work under President Trump's strong leadership to get a peace that lasts."

Trump also said Zelensky told him he was ready to sign a rare earth minerals deal with the US.

Ukraine is yet to comment on the letter.

The US president also said there had been "serious discussions" with Russia, and he'd "received strong signals that they are ready for peace".

Trump did not indicate when the talks took place, or whether he was personally involved in them.

"It's time to end this senseless war. If you want to end wars, you have to talk to both sides," he added.

Earlier on Tuesday, Zelensky described the White House showdown with Trump as "regrettable" in the wake of the US announcing a pause in military aid to Kyiv.

Zelensky said "it was time to make things right", after Trump had accused him of not being ready to come to the negotiating table.

The Ukrainian leader also outlined the first stages of how the war could be ended.

The Oval Office meeting between Zelensky and US officials last week was due to conclude with the two parties signing a deal that would grant the US access to rare earth minerals in Ukraine.

After the clash, which saw Trump accuse Zelensky of "gambling with World War Three", the Ukrainian delegation left without signing the deal. Trump told Zelensky: "Come back when you're ready for peace."