President Obama on Tuesday denounced Donald Trump in his strongest terms yet, calling him “unfit to serve” and “woefully unprepared to do this job” – while the Republican nominee responded by hammering the president’s record and saying November rival Hillary Clinton is the one who has “proven herself unfit to serve in any government office.”

In a written statement released Tuesday afternoon, Trump countered that Obama and Clinton have “single-handedly destabilized the Middle East” while putting the “country at risk” with Clinton’s use of a private email server.

“She is reckless with her emails, reckless with regime change, and reckless with American lives,” Trump said.

Earlier, Obama lit into the GOP nominee while fielding a question on Trump at the top of a White House press conference with the visiting prime minister of Singapore. Obama diverted from the central topic of that visit – moving along the controversial Trans Pacific Partnership trade deal, which Trump opposes – to fundamentally question whether the federal government could function properly if Trump wins.   

“I think the Republican nominee is unfit to serve as president,” Obama said, adding, “He keeps on proving it.”

The president questioned whether Trump has “basic knowledge” on key issues. He went on to say that with past Republican nominees – including his former rivals John McCain and Mitt Romney – he never had doubts about their ability to do the job of president even though they disagreed on policy.

“Had they won I would have been disappointed, but I would have said to all Americans, this is our president,” Obama said, noting he was confident they would abide by certain rules and observe “basic decency.”

Obama added: “But that’s not the situation here.”

The statements mark yet another escalation in the war of words between leading Democrats – namely, party presidential nominee Hillary Clinton and Obama – and Trump on the heels of both parties’ conventions.

The president used his remarks Tuesday in part to pressure top elected Republicans to abandon Trump entirely. For the most part, leading Republicans have repeatedly criticized Trump’s more controversial statements – including his criticism of the Muslim parents of a U.S. Army captain killed in Iraq – but have not disavowed the nominee himself.

“There has to come a point at which you say enough,” Obama said.

Meanwhile, Trump ratcheted up the rhetoric on his end, while aiming his criticism more at Clinton than Obama.

At a rally in Democratic VP nominee Tim Kaine’s home turf of Virginia, Trump on Tuesday mocked Clinton for her talk on Russia.

“She wants to play the tough one … she’s not tough,” he said.

He asked the crowd, “Does she look presidential?” The crowd yelled back, “No!”

He also cited her widely challenged claim to “Fox News Sunday” that the FBI director determined her statements on her personal email use were “truthful.”

“She lied, pure and simple,” Trump said.

The comments came after Trump, on Monday, called Clinton “the devil” and warned that the November presidential election could be “rigged.” 

"I'm afraid the election is going to be rigged, I have to be honest," the Republican nominee told a town hall crowd in Columbus, Ohio, on Monday. He added that he has been hearing "more and more" that the election may not be contested fairly, though he did not elaborate further.

Speaking at a stop Monday night in Pennsylvania, Trump did not mince words as he also blasted Sen. Bernie Sanders for backing Clinton.  

“If he would have just not done anything, go home, go to sleep, relax, he would have been a hero. But he made a deal with the devil. She's the devil. He made a deal with the devil. It's true,” Trump said.

The Associated Press contributed to this report.