ARLINGTON, Virginia (Reuters) -U.S. Treasury Secretary Scott Bessent said on Monday the Federal Reserve is and should be independent but said it had "made a lot of mistakes" and defended President Donald Trump's right to fire Fed Governor Lisa Cook over allegations of mortgage fraud.

Trump has criticized the Fed and its chair, Jerome Powell, for months for not lowering interest rates, and recently took aim at Powell over a costly renovation of the bank's Washington headquarters.

"The Fed should be independent. The Fed is independent, but I, I also think that they've made a lot of mistakes," Bessent told Reuters in an interview at a diner in suburban Washington.

Asked whether the administration's efforts to remove Cook looked like an attempt to give Trump a chance to appoint a majority on the board of governors, Bessent said: "Well, or is it you're having to do the Fed's job for 'em?"

Independent central banks are widely seen as crucial to a stable global financial system.

Bessent said the makeup of the Fed board - with regional bank governors - meant the president could not "stack the board."

Bessent rejected the idea that markets were disturbed by the Trump administration's actions. "(The) S&P's at a new high and bond yields are fine. So we haven't seen anything yet," he said.

Bessent said he believed that Cook should be removed or step down if the allegations against her are true, and noted that she had not denied them.

Trump last week fired Cook, the first Black woman to serve on the Federal Reserve Board of Governors, after the Trump-appointed head of the U.S. Federal Housing Finance Agency, William Pulte, accused her of mortgage fraud. Pulte asked the Justice Department to investigate the claim. The department has not filed charges against her.

Cook and her supporters contend that the fraud allegations are a pretext to remove her so Trump could appoint an ally to the central bank who would promote his policy wishes. Cook is suing Trump and the Fed, saying Trump did not have the legal authority to remove her.

The Trump administration says Cook described separate properties in Michigan and Georgia as primary residences on mortgage applications in 2021, which could have given her preferential interest rates. Cook has said that even if the allegations were true, they would not be grounds for removal because the alleged conduct occurred before she was confirmed by the Senate and took office in 2022.

"I've been very surprised that the Fed has not done an independent review," Bessent said. "She hasn't said she didn't do it. She's just saying the president can't fire her. There's a big difference."

Bessent said the Senate should act quickly to confirm Stephen Miran, chairman of the White House Council of Economic Advisers, for a temporary post, replacing Adriana Kugler who resigned on August 1.