President Obama strongly criticized Donald Trump's suitability for president during an August 2 news conference at the White House. (Reuters)

President Obama on Tuesday escalated his criticism of Donald Trump, calling him “unfit to serve as president,” as the Republican presidential nominee faced censure from members of both parties for disparaging the parents of a fallen army captain.

“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 around critical issues in Europe, in the Middle East, in Asia, means that he is woefully unprepared to do this job,” Obama said at the White House, during a news conference with the prime minister of Singapore.

Obama also challenged Republican leaders to go beyond distancing themselves from Trump, saying their objections “ring hollow” as long as they still pledge to vote for him.

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

Reflecting on the novelty of his own remarks, Obama said his warning stands apart from his criticism of his own Republican presidential rivals, Sen. John McCain (R-Ariz.) and former Massachusetts governor Mitt Romney, with whom he disagreed on “certain policy issues” but whose qualifications and “basic decency” he didn’t dispute.

A U.S. military mother got booed at a campaign rally for Republican vice presidential nominee Mike Pence (R-Ind.) when she asked about Trump's recent attacks on the Muslim parents of a decorated American soldier, Capt. Humayun Khan, who was killed in Iraq. (Reuters)

“And had they won, I would have been disappointed, but I would have said to all Americans . . . this is our president, and I know they’re going to abide by certain norms and rules and common sense,” Obama said. “But that’s not the situation here.”

The president’s remarks pinpointed Republican divisions. He also made clear that Democrats have disagreements of their own, by underscoring his commitment to the 12-nation Trans-Pacific Partnership. The Democratic candidate he hopes will succeed him, Hillary Clinton, opposes the deal, which is awaiting ratification in Congress.

“Right now I’m president, and I’m for it,” Obama said.

Obama’s was the latest in a volley of complaints this week against Trump, whose campaign responded in a statement denouncing the president as a “failed leader” who has wreaked havoc around the world.

Bipartisan and among the most sustained of the election cycle, the criticism of Trump has mainly been a response to his denigration of Khizr and Ghazala Khan, immigrants from Pakistan who appeared last week at the Democratic National Convention to denounce him for his harsh rhetoric about Muslims. They said their son, who was killed in Iraq, would have been barred from entering the country under Trump’s proposed ban.

But the broadsides have also focused on the nominee’s comments about foreign relations, including his apparent ignorance of Russia’s annexation of the Ukrainian territory of Crimea in 2014 and his appeal to Russian actors to expose Clinton’s emails.

In response, Trump has laughed off concerns about his overtures to Russian President Vladi­mir Putin, saying warmer relations would help the United States pursue its international objectives, such as defeating Islamic State militants.

At a campaign event Tuesday in Ashburn, Va., Trump attacked Clinton for having a poor relationship with Putin, saying: “This is a nuclear country we’re talking about. Russia. Strong nuclear country.”

“Their stuff is newer . . . they have a lot more,” he said. “She wants to play the tough one. She’s not tough.”

Meanwhile, a Kremlin spokesman told NBC News this week that Putin has never had any contact with Trump, which is in line with a recent statement by Trump that he has not spoken to Putin — and yet in direct conflict with the real estate mogul’s prior declarations, including in 2014 at the National Press Club, when Trump said he had been in Moscow and had spoken, “indirectly and directly,” with the Russian president.

In his hour-long remarks on Tuesday, delivered at a local high school, Trump repeated his grave warnings about immigration — across the southern border from Mexico as well as from countries beset by Islamic radicalism. Because “we don’t know if they’re ISIS,” Trump said of migrants from the Middle East, the result would be “the all-time great Trojan horse.”

He didn’t mention the Khans, who have proven themselves dogged in their campaign against Trump, or new evidence that the candidate’s approach is driving a wedge in the Republican Party. Rep. Richard Hanna (R-N.Y.) on Tuesday became the first sitting Republican member of Congress to say publicly that he plans to vote for Clinton, declaring in an interview with Syracuse.com that Trump is a “national embarrassment.”

The three-term congressman, who represents a swath of upstate New York near Syracuse but is not running for reelection this year, has bucked his party in the past on issues ranging from gay marriage to climate change. He declared his support for Clinton in an opinion piece published Tuesday on the news website and elaborated in an interview that Trump’s prolonged feud with the parents of a Muslim American Army captain killed in Iraq was the final straw.

“I saw that and felt incensed,” Hanna said in the interview. “I was stunned by the callousness of his comments.”

He added: “I think Trump is a national embarrassment. Is he really the guy you want to have the nuclear codes?”

Hanna had already said he would not vote for Trump — a stance shared by a handful of his Republican colleagues. But his pronouncement that he would therefore support Clinton, a woman reviled by much of his party, dealt yet another blow to Trump as his poll numbers dip in the wake of the conventions and as his campaign struggles under mounting criticism over his response to the Khans, whose son Humayun was killed in 2004, at age 27, by a car bomber in Iraq.

Trump said Khizr Khan had “no right” to assail him and suggested that Ghazala Khan was barred by her Muslim faith from speaking alongside her husband.

The quarrel continued into this week, as Trump tweeted that Khan had “viciously attacked” him and had shifted focus from the real concern, “RADICAL ISLAMIC TERRORISM.” The GOP nominee faced strong criticism from a bipartisan group of decorated combat veterans, members of Congress and family members of slain soldiers. A particularly lengthy and impassioned rebuke came from McCain, the Senate Armed Services Committee chairman, who was a prisoner of war in Vietnam.

“While our party has bestowed upon him the nomination, it is not accompanied by unfettered license to defame those who are the best among us,” McCain said.

On Tuesday, Trump addressed the matter only implicitly, faulting the media for not giving enough attention to Patricia Smith, a Trump supporter who is the mother of a victim of the Benghazi attacks, while giving “other people unbelievable amounts of air.” In fact, multiple networks, including CNN and MSNBC, carried Smith’s speech at the Republican National Convention live, while Fox News — whose host, Brian Kilmeade, criticized other networks for not covering Smith — did not.

Trump also said his critics would never desert him because they fear a Supreme Court stacked with Clinton appointees. He recounted his own comments from a campaign stop in Pennsylvania, in which he said he told his audience that “even if people don’t like me, they have to vote for me.”

“I said, even if you can’t stand Donald Trump, you think Donald Trump is the worst, you’re going to vote for me. You know why? Justices of the Supreme Court,” he said. “If they pick judges, we’re going to end up with another Venezuela, except just a bigger version.”

With a bit of stagecraft, Trump also appeared to try to fend off questions about his military acumen — and his own draft deferments during the Vietnam War — by beckoning onto the stage a lieutenant colonel. The man had given him his Purple Heart medal before the rally as a vote of “confidence,” Trump said.

“I always wanted to get the Purple Heart,” Trump said. “This was much easier.”