"I think the Republican nominee is unfit to serve as president," Obama said at a White House news conference. "I said so last week. He keeps proving it."
Obama added that Trump has shown he is "woefully unprepared to do this job" after his comments on military families as well as his handle on foreign affairs.
He slammed Trump for his rhetoric, including the one against parents of a slain Muslim-American soldier, and said the Republican presidential nominee doesn't have the judgment, temperament or understanding to be the president of the country.
"There has to come a point at which you say enough," Obama said of the Republican leaders leaders
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"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," the president said at the White House.
Obama remarked that Republican denunciations of Trump "ring hollow" as they continue to endorse Trump.
Obama said this opinion of Trump is shared by prominent
Republicans.
"I think what's been interesting is the repeated denunciations of his statements by leading Republicans, including the speaker of the House and the Senate majority leader and prominent Republicans like John McCain," he said.
"There has to be a point in 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," Obama said.
At some point, Republicans should realise that Trump has gone too far and that the things he says indicates he "doesn't have the judgment, the temperament the understanding to occupy the most powerful position in the world," Obama said.
While Obama said he has disagreed with former Republican presidents on policy issues, he did not have a doubt that they could function as president."
"I recognise that they all profoundly disagree with myself or Hillary Clinton on tax policy or on certain elements of foreign policy. But you know, there have been Republican presidents with whom I disagreed with but I didn't have a doubt that they could function as president," Obama said.
Obama explained that had he lost to Mitt Romney or McCain, he certainly "would have been disappointed," but that he would have conceded and had the confidence that they would "abide by certain norms and rules and common sense, will observe basic decency."