President Barack Obama has said Republican nominee Donald Trump is unfit to be president, and questioned why his party still supports the New York billionaire's candidacy.
"There has to come a point at which you say: 'Enough'," Mr Obama said.
Mr Trump has been sharply criticised for attacking the parents of a fallen US soldier who spoke out against him.
He has also been condemned for backing the Russian annexation of Crimea.
Mr Obama said he had had policy differences with previous Republican presidents and candidates - but added that he had never thought they could not function as president.
At last week's Democratic National Convention, Khizr Khan - a Muslim whose son was killed serving in the US military in Iraq - criticised Mr Trump's plan to temporarily ban Muslims from entering the US.
Mr Trump responded by attacking the "Gold Star" family, the term for families that have lost a relative in war. Democratic and Republican leaders as well as veterans' groups quickly condemned him.
"The Republican nominee is unfit to serve as president and he keeps on proving it," Mr Obama said.
"The notion that he would attack a Gold Star family that made such extraordinary sacrifices... means that he is woefully unprepared to do this job."
Mr Obama also took to task Republican leaders who have frequently clashed with Mr Trump over this statements and policies about women, undocumented immigrants and Muslims.
"What does this say about your party that this is your standard bearer?" Mr Obama asked Republicans. "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."
Top Republican leaders such as House Speaker Paul Ryan and Senate Majority Leader Mitch McConnell have been highly critical of Mr Trump, but the billionaire has retained their support.
Mr Trump quickly hit back at the president and Mrs Clinton, whom he often says is running for Obama's third term, as embracing policies that have destabilized the Middle East, hurt veterans and shipped American jobs overseas.
"They have betrayed our security and our workers, and Hillary Clinton has proven herself unfit to serve in any government office," Mr Trump said in a statement.
Mr Obama said that even if he had lost his White House races in 2008 and 2012, he would not have doubted his Republican rivals' ability to lead the country.
That was not the case for Mr Trump, Mr Obama said.
"There has to come a point at 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," Mr Obama said.
Yesterday, New York Representative Richard Hanna became the first Republican member of Congress to publicly say he would vote for Democrat Hillary Clinton. Mr Hanna said Mr Trump's comments about the Khan family were the deciding factor.
Until recently, many Republicans opposed to Mr Trump had stopped short of supporting Mrs Clinton, saying they would vote for a third party or write-in candidate.