The Senate Banking Committee will proceed with confirmation hearings for Kevin Warsh, President Donald Trump's pick to head the Federal Reserve, despite a key senator's hold on the nomination, Treasury Secretary Scott Bessent said on Friday.

"I think it is important that we get to the hearings. Chair (Jerome) Powell's term ends mid May, and anyone who cares about the integrity, the independence of the Fed is going to want to see continuity with Kevin Warsh," Bessent told CNBC's "Squawk Box" program.

Republican lawmaker Thom Tillis has said he supports Warsh's candidacy, but will hold up a vote on any Fed nominee while the Justice Department continues to investigate Powell over a large Fed renovation project that is over budget.

Bessent said he had proposed during a meeting with Senate Republicans on Tuesday that the Senate Banking Committee carry out its own investigation of the Fed's renovation of its Washington headquarters, but declined to comment on whether that could replace the Justice Department investigation and prompt Tillis to release his hold.

Senate Banking Committee Chairman Tim Scott has said he does not believe Powell committed a crime.

Bessent noted that Scott, who represents Bessent's home state of South Carolina, had said he believed Powell was "guilty of one thing, incompetence and this building project is out of control, way over budget."

Powell last month disclosed the criminal probe into his statements to the Senate about the Fed's renovations, describing it as part of the Trump administration’s "threats and ongoing pressure" on the Fed to cut rates. Tillis on Thursday told reporters that his hold on Fed nominees remains in place “until the investigation is brought to a conclusion.”

“That happens one of two ways: they cease the investigation, say there's no there there, or they give me compelling information that says I was wrong," Tillis said.