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 last year said the cost of the Fed's building renovations had run too high, as part of a long-standing feud with Powell.

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

"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.