"He's woefully unprepared to do this job," President Obama said of Donald Trump

President Barack Obama is doubling down on his declaration that Donald Trump is “unfit” for the presidency – because, Obama says, the GOP nominee “keeps on proving it.”

Speaking alongside Singapore Prime Minister Lee Hsien Loong at a press conference in the White House East Room on Tuesday, Obama denounced Trump’s treatment of the family of a slain Muslim U.S. solider, and criticized his apparent lack of knowledge about world affairs. “Yes, I think the Republican nominee is unfit to serve as president,” Obama said. “I said so last week, and he keeps on proving it.”

“The notion that he would attack a Gold Star family that had 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’s woefully unprepared to do this job,” the president added.

His criticism was not reserved for Trump alone. Obama also lambasted Republicans for continuing to support Trump, saying, “There has to be a point at which you say, ‘Enough.’ ”

“What does this say about your party that this is your standard-bearer?” Obama asked GOP leaders. “This isn’t a situation where you have an episodic gaffe. This is daily and weekly where they are distancing themselves from statements he’s making. There has to be a point at which you say, ‘This is not somebody I can support for president of the United States, even if he purports to be a member of my party.’ ”

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The president added that Republicans who have distanced themselves from Trump’s comments but failed to revoke their endorsements of him are not doing enough.

“I don’t doubt their sincerity. I don’t doubt they were outraged by some of the statements that Mr. Trump and his supporters made about the Khan family,” Obama said. “But there has to come a point in which you say, ‘Somebody who makes those kinds of statements doesn’t have the judgment, the temperament, the understanding to occupy the most powerful position in the world.’ ”

Trump has come under bipartisan fire for his criticism of the family of Muslim American U.S. Army Capt. Humayun Khan. After the fallen soldier’s father, Khizr Kahn, said at the Democratic convention on Thursday that Trump had “sacrificed nothing and no one,” the GOP nominee claimed he’d been “viciously attacked” and suggested that Khizr’s wife, Ghalaza, didn’t make her own remarks because she was forbidden as a Muslim woman.

Republicans including Arizona Sen. John McCain spoke out against Trump following the controversy. But Senate Majority Leader Mitch McConnell and House Speaker Paul Ryan, who were asked by Khizr Khan to repudiate Trump, issued statements distancing themselves from the GOP nominee’s remarks but did not withdraw their support for him.