US President Donald Trump has threatened to fire Federal Reserve Chair Jerome Powell if he does not step aside at the end of his term in May.

The two have been embroiled in a bitter spat over Powell's reluctance to cut the central bank's interest rate, despite Trump's repeated calls.

Powell's term expires on 15 May, but he plans to remain in post until his successor, Kevin Warsh, is confirmed by the Senate.

Then I'll have to fire him, Trump told Fox Business, when asked about Powell's plans to stay on in the job.

I've held back firing him. I've wanted to fire him, but I hate to be controversial, Trump said.

Thom Tillis, an influential Republican senator on the committee which oversees nominations for the Federal Reserve chair, has threatened to block Warsh's confirmation. If Warsh is not confirmed before Powell's term expires, he plans to stay on temporarily in the post.

That's what the law calls for. That's what we've done on several occasions, Powell has said.

Tillis has warned Trump he will not allow Warsh's appointment to proceed unless a criminal investigation into Powell, linked to the renovation of the Federal Reserve building, is dropped.

Trump expressed hope that Tillis would withdraw his opposition to the appointment, emphasizing that he believes Tillis understands the importance of moving forward.

However, Trump has made it clear he is not willing to drop the investigation into Powell. He stated, Don't you think we have to find out what happened there? I have to find out.

Accusing Powell of mishandling the Federal Reserve renovation project that allegedly overspent millions, Trump has referred to Powell as a knucklehead and criticized his decisions regarding interest rates.

The tensions have had tangible effects, with stock markets and the US dollar responding negatively to news of Trump's potential dismissal of Powell.

If Trump were to dismiss Powell, it would set a significant precedent, marking the first time a Federal Reserve chair has been fired.

Appointed by Trump in 2017, Powell was meant to be a stabilizing force during Trump’s first term but has since fallen out of favor with the former president.