President Donald Trump says he is “highly unlikely” to fire Federal Reserve Chair Jerome Powell, but that he would welcome Powell's resignation, in public statements made less than 24 hours after suggesting in a private meeting that he was leaning in favour of dismissing the head of the nation's central bank.

Trump confirmed that in a White House meeting Tuesday night with about a dozen House Republicans he had discussed the “concept” of dismissing Powell, long a target because of his refusal to lower interest rates as Trump wants.

“Almost every one of them said I should,” Trump said about the lawmakers who had come to talk to him about crypto legislation.

He indicated he was leaning in that direction, according to a White House official. During that session, Trump waved a letter about firing Powell, but a person familiar with the matter said it was essentially a prop drafted by someone else and that the Republican president has not drafted such a letter.

Neither source was authorised to publicly discuss the private meeting and they spoke only on condition on anonymity.

Trump made his comment about being “highly unlikely” to dismiss Powell — ”unless he has to leave for fraud” — during an Oval Office meeting with Salman bin Hamad Al Khalifa, the crown prince of Bahrain.

Later,  in an interview with the Real America's Voice network, Trump said he would love for to resign but acknowledged that many have said it would disrupt the markets if the president were to remove him.

"I'd love if he wants to resign, that would be up to him. They say it would disrupt the market if I did," Trump said

Powell, who was nominated by Trump in late 2017 to lead the Fed and then nominated for a second term by then-President Joe Biden four years later, has said he intends to serve out his term as Fed chief, which ends on May 15.

In recent days, White House and administration officials have accused Powell of mismanaging a $2.5 billion renovation project at the Fed, adding to months of efforts by Trump try to rid himself of the politically independent central banker.

US stocks were shaky as Trump spoke about Powell on Wednesday. The S&P 500's modest gain in the morning became a drop of 0.7 per cent after initial reports that the president may fire the Fed chair. Stocks then trimmed their losses after Trump's later comment.

Treasury yields also swivelled in the bond market but remained mostly calm.

Those at the White House meeting were among the more far-right lawmakers, including members of the House Freedom Cause whose views are not always shared by other Republicans. In the Senate, Republicans have taken a more guarded approach. Some have backed Powell’s performance at the Fed as they await an inspector general's review of the construction project.

Federal Reserve Chair Jerome Powell has said he plans to serve out his term - AP

In a speech Wednesday, North Carolina Senator Thom Tillis said if Powell is dismissed, “you are going to see a pretty immediate response”.

“If anybody thinks it would be a good idea for the Fed to become another agency in the government subject to the president, they’re making a huge mistake," said Tillis, who has announced that he is not running for reelection.

Louisiana Senator John Kennedy said this week that Powell “has done a decent job.”

"I don’t think he’s been perfect,” he said, adding that there have been times they disagreed, but “I do believe that the chairman is calling them like he sees them”.

Republicans on the House Financial Services Committee had been scheduled to meet with Powell on Wednesday evening in a gathering set months ago, but it was abruptly cancelled due to votes in the House, according to a committee aide granted anonymity to discuss a private meeting.

US stocks clawed back into positive territory after the president swiftly denied reports of a Federal Reserve shakeup.

The main US stock indexes fell sharply earlier, the dollar plunged and Treasury yields rose after Bloomberg News reported the possibility of replacing Powell.