Trump criticized Obama in an interview with WJLA hours after Obama had declared at a news conference that Trump is "unfit to serve as president."
"Well, he's a terrible president," Trump said. "He'll probably go down as the worst president in the history of our country, he's been a total disaster."
Trump pointed to the Middle East, and Obama's failure to enforce "his line in the sand" in Syria over the use of chemical weapons, as evidence of the President's foreign policy failures.
"I think it just means he's concerned I'm going to win," Trump said. "Don't forget, last time he said I would never get the nomination, now he's saying I wouldn't get the election now all of the sudden he said the other day maybe I can win the election."
The strong rebuke in the White House East Room came after Trump's criticism of the family of a slain Muslim US soldier, along with comments that displayed apparent confusion related to the Russian incursion into Ukraine.
"The Republican nominee is unfit to serve as president," Obama said at a White House news conference alongside the Prime Minister of Singapore. "He keeps on proving it."
Obama described his feelings about Trump as unprecedented, recalling disagreements with previous GOP presidential nominees Sen. John McCain and Mitt Romney -- but never an outright sense they were unfit to serve.
"The notion that he would attack a Gold Star family that made such extraordinary sacrifices on behalf of our country, the fact that he doesn't appear to have basic knowledge of critical issues in Europe, the Middle East, in Asia, means that he's woefully unprepared to do this job," Obama said.
Obama said there are now weekly episodes in which even Republican Party leaders distance themselves from Trump.
"There has to be a point at which you say, 'Enough,'" Obama said.