Trump said on Monday he was "not thrilled" with Jerome Powell's rate hikes and said the U.S. central bank should do more to help him to boost the economy.
American presidents rarely criticize the Fed, whose independence is considered important for economic stability. But Trump has made reducing U.S. trade deficits a priority, and the combination of rising interest rates and a strengthening dollar poses risks for export growth.
"It would appear that Mr Trump would like to keep the U.S. dollar a little on the weak side in order to remain competitive," said CMC Markets chief markets analyst David Madden.
"But given the dollar has been in demand recently on account of geopolitical issues and the Fed's monetary tightening policy, he might find it difficult to talk the greenback lower."
The dollar index against a basket of six other currencies fell 0.3 percent to 95.596 as of 0730 GMT after touching 95.440, its lowest since Aug. 9.
Escalating trade tensions between the United States and its trading partners and a plunge in the Turkish lira have pushed the dollar index up recently.
But the greenback weakened on Tuesday as investors ditched it as a safe haven before China and the United States hold talks this week that may help ease their dispute over trade.
Trade tensions have on the whole helped the dollar, which benefits from geopolitical turmoil as the market seeks out less risky investments.
"It looks as though Trump's comments have caught the market very long dollar after last week's emerging market rout," said Chris Turner, head of currency strategy at ING in London.
The Fed has raised interest rates twice this year and is expected to do so again next month.
Traders are preparing for the release of Federal Reserve policy meeting minutes on Wednesday and an annual Jackson Hole symposium for insights into the direction of U.S. monetary policy.
Against the U.S. currency, the euro strengthened 0.3 percent to a daily high of $1.154.
Concerns that a currency crisis in Turkey would hurt euro zone banks and uncertainty about the Italian government's planned budget have weighed on the euro recently.
Trump's remarks appeared to bolster appetite among investors for the Japanese yen as a safe haven of choice.
The yen was basically flat at 110.08 yen, paring gains after touching as high as 109.775 yen earlier.
The dollar on Tuesday fell below the psychologically-significant 110-yen level for the first time since June 28.
The Australian dollar was 0.13 percent higher at $0.7350, after Prime Minster Malcolm Turnbull survived a leadership vote by a narrow margin.