The Fed made the decision despite Mr. Trump tweeting on Tuesday that it should reduce rates by 1% to help the US economy "go up like a rocket".
The Fed indicated earlier this year that it would not change rates for the rest of 2019.
In his latest attack on the Fed, Mr.Trump criticized the central bank for "incessantly" raising rates.
He said that although growth is strong at 3.2% in the first quarter, if the Fed cut interest rates "with our wonderfully low inflation, we could be setting major records".
Commenting on whether comments such as these affect the Fed's decisions, chairman Jerome Powell said: "We are a non-political institution and that means we don't think about short-term political considerations, we don't discuss them and we don't consider them in making our decisions one way or the other."
In a statement explaining its decision, the Federal Open Market Committee (FOMC) maintained its "patient" approach to interest rates.
It said that economic activity rose at a "solid rate" but said that "growth of household spending and business fixed investment slowed in the first quarter".
It also noted that inflation is below the Fed's target of 2%.
Inflation growth slowed to 1.6% in the year to March compared with 1.7% in February,
Mr. Powell said the FOMC had "good reasons" to think that lower inflation growth "may wind up being transient".
But he said: "We did see inflation running persistently below, then that's something the committee would be concerned about."
At present, Mr. Powell said the Fed is "comfortable" with its current stance.