"You start whining before the game's even over?" Obama said during a news conference in the White House Rose Garden, adding that Trump's claim is "not based on facts."
Trump and his surrogates have increasingly claimed the US election system is "rigged," coming after two lackluster debate performances and a drop in poll numbers nationally and in key swing states. He's urged his supporters to monitor polling sites for potentially ineligible voters attempting to cast ballots.
The rhetoric has been brushed off even by Republican governors, who say there are no signs of corruption in their states' voting systems.
Obama echoed those sentiments Tuesday, saying there's "no serious person out there who would suggest somehow that you could even rig America's elections."
And he claimed Trump's warnings could abrade faith in the US political system.
"One way of weakening America and making it less great is if you start betraying those basic American traditions that have been bipartisan and have helped to hold together this Democracy now for well over two centuries," Obama said.
He derided Trump's remarks as reflective of an unpresidential attitude, declaring again that the Republican nominee's temperament was disqualifying.
"It doesn't really show the kind of leadership and toughness that you'd want out of a president. You start whining before the game's even over? If whenever things are going badly for you and you lose you start blaming somebody else? Then you don't have what it takes to be in this job," Obama said.
And he said the warnings of a "rigged election" are entirely unprecedented in modern American political history.
"I have never seen in my lifetime or in modern political history any presidential candidate trying to discredit the elections and the election process before votes have even taken place. It's unprecedented," Obama said alongside Italian Prime Minister Matteo Renzi.
Trump has at times embraced the label of "whiner," telling CNN in an interview last year, he is "the most fabulous whiner."
"I do whine because I want to win and I'm not happy about not winning and I am a whiner and I keep whining and whining until I win," Trump told CNN's Chris Cuomo in August 2015.
Long feud with Trump
It was Obama's latest salvo in what's become a bitterly negative campaign against Trump. At the beginning of Tuesday's news conference, Obama said he planned to be "a little more subdued" in his discussion of Trump, given the diplomatic setting just outside the Oval Office.
And while he didn't slip into his campaign cadences, he unleashed a harsh rebuke of the Republican candidate, describing his behavior as "unprecedented" on multiple fronts.
Obama called Trump's "flattery" of Russian President Vladimir Putin "out of step" with US norms, and called out Republicans who support their nominee as hypocritical.
"You'll have to explain to me how it is that some of the same leaders in the Republican Party who were constantly haranguing us for even talking to the Russians and who consistently took the most hawkish approaches to Russia, including Mr. Trump's selection for vice president, now reconcile their endorsement of Mr. Trump with their previous views," he said.
But he reserved his harshest rhetoric for Trump's assertions about the upcoming election.
"I'd advise Mr. Trump to stop whining and go try to make his case to get votes," Obama said. "And if he got the most votes, then it would be my expectation of Hillary Clinton to offer a gracious concession speech and pledge to work with him in order to make sure that the American people benefit from an effective government, and it would be my job to welcome Mr. Trump, regardless of what he said about me, or my differences with him on my opinions, and escort him over to the Capitol, in which there would about peaceful transfer of power."
"That's what Americans do," Obama said.