The US justice department is dropping its investigation into the Federal Reserve chairman, Jerome Powell, over alleged building cost overruns.

US Attorney Jeanine Pirro said instead there would be an internal investigation led by the central bank's inspector general.

President Donald Trump has said the cost of the Fed's building renovations were too high, as part of a long-standing feud with Powell.

Powell's term is nearing its end and the US Senate is considering Trump's nominee for his replacement, Kevin Warsh. A key Republican, Thom Tillis, has withheld his support for Warsh unless the Trump administration would drop its investigation into Powell.

"American taxpayers deserve answers about the Federal Reserve's fiscal mismanagement, and the Office of the Inspector General's more powerful authorities best position it to get to the bottom of the matter," said White House spokesman Kush Desai in a statement.

"The White House remains as confident as before that the Senate will swiftly confirm Kevin Warsh as the next Federal Reserve Chairman to finally restore competence and confidence in Fed decision-making."

Trump called for the Fed to lower interest rates after returning to office last year, and then began floating the idea of firing Powell - a step some said could be illegal.

Amid months of attacks, he branded Powell a "knucklehead" and claimed he was "doing a lousy job" after his repeated calls for rate cuts were ignored.

Last summer, Trump criticised the ballooning costs of the renovations, arguing it will cost $3.1bn (£2.3bn), much higher than the Fed's $2.5bn forecast. The Fed has said the renovations will reduce its costs over time.

Powell took the highly unusual step of releasing a video in January disclosing that the justice department had served the Fed with subpoenas and threatened a criminal indictment over testimony he gave to a Senate committee about renovations to Federal Reserve buildings.

Calling the investigation "unprecedented", Powell said he believed it was opened due to Trump's anger over the Fed's refusal to cut interest rates despite repeated public pressure from the president. Trump said he did not "know anything" about the investigation.

It marked the first time Powell had publicly and robustly pushed back against the US president, as he warned that the independence of the US central bank was at stake.

"This is about whether the Fed will be able to continue to set interest rates based on evidence and economic conditions, or whether instead monetary policy will be directed by political pressure or intimidation," Powell said.

Lower interest rates make it cheaper to borrow, while higher rates dampen spending activity, helping to keep prices stable.

Trump, who cut his teeth professionally taking out loans as a property developer, has long confessed to liking a low interest rate policy.

He objected when the Fed raised rates in his first term, and has argued keeping rates too high could do unnecessary economic damage.

The Fed buildings being renovated are the Eccles and 1951 Constitution Avenue. The "overhaul and modernisation" will be the first works since they were constructed in the 1930s, and includes removal of asbestos and lead contamination.

Powell was nominated by Trump for the role as Fed chair in 2017 during his first term as president.

Last week, Trump threatened to fire Powell if he does not step aside at the end of his term next month.

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