Mnuchin was asked about Trump's tweet Sunday that if the Fed had done its job properly, the stock market would be 5,000 to 10,000 points higher and overall growth would have been "well over" 4% last year instead of 3%.
Interviewed by Fox Business, Mnuchn said, "In my role as secretary, it is inappropriate for me to comment. I do think that the Fed independence is something that the world looks to, and I think that the dollar being the reserve currency is very important."
The dollar's standing as a reserve currency used by other nations brings significant economic advantages to the United States in the area of trade and the willingness of foreigners to help finance the federal government's $22 trillion national debt.
Trump's attacks on the Fed increased sharply as a string of four Fed rate hikes triggered a sharp sell-off in the stock market late last year. The Fed has since reversed course. It has signaled that it expects to keep rates unchanged for the entire year.
Trump, however, has demanded that the Fed do more to support the economy by starting to cut rates. He has also said he intends to nominate two political allies, conservative commentator Stephen Moore and former pizza executive and 2012 GOP presidential candidate Herman Cain, to two vacancies on the seven-member Fed board.
Both of those proposed nominations have come under attack. Critics charge that Trump would do serious harm to the Fed's political independence by putting close allies on the Fed board.
But Larry Kudlow, head of the president's National Economic Council, said Monday that Trump considered himself a "disruptor" who wanted to put his stamp on the Fed. "These are unconventional appointments. We'll see what happens with them," he said in a separate Fox interview.
Charles Evans, president of the Fed's Chicago regional bank, said in a CNBC interview Monday, that what was important to protect the Fed's credibility is for the officials at the Fed to keep making interest-rate decisions based on the economic data.
"As long as we keep looking at the data, can explain it relative to what we are supposed to be doing, we just have to accept criticism," Evans said.
With inflation remaining below the Fed's 2 percent target, Evans said he could see the central bank keeping rates unchanged not only for the rest of this year but into the fall of 2020.
AP White House reporter Darlene Superville contributed to this report.
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