Trump told CNBC he's anxious the Fed's policies will cancel out his efforts to boost the economy.
The president also noted he is doing what's right for the American people and reiterated his long-held belief about the state of US trade with China.
He likewise also took aim at the dollar, saying a higher value "puts us at a disadvantage" and adding that the Chinese yuan "has been dropping like a rock".
"I don't necessarily agree with it, because he's raising interest rates ..."
The U.S. dollar index .DXY cut its gains after Trump's comments, while yields on U.S. Treasury securities hit session lows. "But at the same time I'm letting them do what they feel is best", he said.
The president acknowledged that his comments about the Fed would likely raise concerns.
Nixon pressured the new Fed chairman to keep interest rates low to help maintain lower unemployment.
The central bank is an independent agency and usually the commander in chief doesn't comment directly on Fed policy.
In an interview on CNBC, Trump said, "I'm not thrilled" about the Fed's policy of gradually raising its key interest rates. "The remarks certainly aren't an immediate threat to Fed independence, but they break with the tradition of respectful distance".
While the US economy has been growing robustly with unemployment under 4% and inflation in check, the Fed hasn't been a target for the administration.
"Now I'm just saying the same thing that I would have said as a private citizen", said Mr. Trump.
Still, Wall Street took notice of the president's apparent desire for a weaker dollar.
"Following falls in U.S. shares and ahead of the weekend, sales for position-adjustment reasons are seen overwhelming the market", SBI Securities said in a commentary.
TRT World's William Denselow reports from NY.
Randall Kroszner, a former Fed governor, said the central bank has withstood political pressure before and will continue to do so under Powell's leadership.
Asked about the prospect of a stock market plunge in response to larger-scale tariffs, Trump said: "Well, if it does, it does".
With the economy growing at a healthy rate, Powell has said the time is right to normalize interest rates, which have been at historic lows as the economy has recovered. Given Trump's recent Fed picks, this doesn't appear to be the case.