By Agence France-Presse
And in an interview with Reuters, he declined to confirm his support for the central bank's independence, something that has the potential to worry financial markets.
That was a step further than Trump went just a month ago, when he also said he was "not thrilled" with the Fed for raising the key interest rate.
As the US economy has recovered, the Fed has raised the benchmark lending rate seven times since December 2015, twice this year under current Chairman Jerome Powell, and it expected to hike twice more in 2018.
Powell in a radio interview in mid-July said he was not concerned about pressure on him to alter policy, saying "we don't take political considerations into account."
He added at the time that "no one in the administration has said anything to me that really gives me concern on this front."
Trump nominated Powell to lead the Fed after declining to give a second term to Janet Yellen, someone he harshly criticized during the presidential campaign in 2016, accusing her of keeping rates low to help his opponents.
He repeated his criticism of monetary policy under Powell's leadership at a fundraiser on Friday, according to reports by the Wall Street Journal and Bloomberg.
"I'm not thrilled with his raising of interest rates, no. I'm not thrilled," Trump repeated in the interview with Reuters on Monday.
Asked if he believed in Fed independence, Trump said: "I believe in the Fed doing what's good for the country."
Questioning Fed policy is normally off limits for US politicians, since it could raise fears central bankers would fail to act to head off rising inflation. But Trump's has not been a normal administration.
Trump criticism of the Fed "attracted a lot of attention" but did not really move the stock or the bond markets, LBBW market strategist Karl Haeling told AFP.
"So far people don't think it's going to change the Fed's policy, at least for its meeting in September."
Strong US dollar
However, Trump's criticism "has definitely been a driver" of currency markets, according to David Gilmore from Foreign Exchange Analytics.
But "I don't think anybody thinks Powell will be influenced by that."
The dollar index moved slightly lower after the Bloomberg and Wall Street Journal stories and accentuated its drop after Reuters' story.
Powell explained the rationale behind Fed policy in June, when the last rate increase took effect.
While rates remain low, "we think that gradually returning interest rates to a more normal level as the economy strengthens is the best way the Fed can help sustain an environment in which American households and businesses can thrive."
As interest rates rise, the US dollar strengthens as investors pour money into the country in search of higher returns.
That makes US exports more expensive and makes imports cheaper, which will tend to raise the US trade deficit -- the opposite impact that Trump is seeking with his confrontational trade policies that have imposed tariffs on tens of billions in Chinese goods.
Those trade policies in turn, which as of Thursday will impact $50 billion in Chinese products, as well as steel and aluminum exports from around the world, weaken the Chinese currency.
China's renminbi (RMB) has sunk seven percent since June, reaching 6.85 yuan to the US dollar its lowest level since May 2017.