President Donald Trump looks on as his nominee for the chairman of the Federal Reserve Jerome Powell takes to the podium during a press event in the Rose Garden at the White House, November 2, 2017 in Washington, DC.

"I'm not blaming anybody, I put him there," Trump said of Powell. "And maybe it's right, maybe it's wrong. But I put him there."

"Because the Fed is raising rates too fast. And it's independent, so I don't speak to him," Trump said in an interview with Fox Business, referring to Fed Chairman Jerome Powell. "But I'm not happy with what he's doing because it's going too fast. Because – you look at the last inflation numbers, they're very low."

Although Trump has repeatedly said he believes the Fed is "making a mistake" with its monetary policy, he also has said he is "not going to fire" Powell. Trump said in an Oct. 11 interview that he is "just disappointed" with Powell's decisions.

The president's latest attack against the central bank came just hours after the Labor Department reported that the number of job openings in the U.S. economy leaped to a record 7.1 million in August. That's after the government reported earlier in the month that the unemployment rate in September dropped to 3.7 percent, the lowest level in nearly 50 years.

The recent economic data helped the Fed's policy-making arm defend its increase to the federal funds rate in September – which was the such third quarter-point bump this year.

Both the Fed and markets anticipate a fourth rate hike in December. But Trump has continued to vocalize his disagreements with the Fed and that's led some to fear that the institution's independence is at risk. U.S. officials say Trump is honoring the Fed's historic ability to make decisions outside of political interference. Former Fed Chair Janet Yellen said on Friday that she believes the Fed will continue with its economic strategy, even with Trump's open criticism.

"The Fed is certainly not crazy in terms of what it's doing," Yellen reportedly said at the World Knowledge Forum.

Two other prominent officials backed Powell's independence last week, as well: Mark Carney, the governor of the Bank of England Governor and Christine Lagarde, the managing director of the International Monetary Fund. During a CNBC-moderated panel, Carney praised Powell, saying he "is an individual that really understands the plumbing of the U.S. and global financial systems."

Lagarde added that she would not associate Powell with being crazy.

"He comes across and members of his board as extremely serious, solid and certainly keen to base their decisions on actual information and the desire to communicate that properly," Lagarde said.

– CNBC's Tom Franck contributed to this report.

WATCH: Trump says the Fed has gone crazy