Whitson, who has been at the ISS for 534 days and counting, is scheduled to stay there for at least another five months.
Her record surpasses that of fellow American astronaut Jeff Williams.
"That is an incredible record to break, and on behalf of our nation," Trump said during a call to the ISS on Monday morning, "and frankly on behalf of the world, I would like to congratulate you."
Whitson, 57, also holds the record for being the oldest American woman in space, and the first woman to command the ISS twice.
"It is actually a huge honor to break a record like this, but it is also a huge honor for me to be representing all the folks at NASA who make spaceflight possible," Whitson said on the call with the president.
Trump signed a bill in late March to authorize funding for NASA, and to create a plan for putting people on Mars by the 2030s.
Whitson noted that researchers involved in the ISS are studying how to make a Mars mission become a reality by looking at the effects of microgravity on the human body and devising ways of recycling water.