US President Barack Obama, asked about populist billionaire Donald Trump becoming the presumptive Republican presidential nominee, on Friday cautioned: "We are in serious times, and this is a really serious job."

"This is not entertainment," Obama said, taking questions in the White House press room. "This is not a reality show."

Meanwhile, Trump was continuing to try to consolidate support within the fractured Republican Party.

Obama said that Trump had a long record that needed to be examined and urged the press to scrutinize him and not to focus on the "spectacle and the circus."

A candidate whose position on international issues could threaten war or potentially upend US relationships with other countries or harm the financial system, "that needs to be reported on," Obama said.

He said there was no doubt that there was a debate within the Republican party about "who they are and what they represent."

Asked if he followed the inflammatory businessman on social media, Obama said: "As a general rule, I don't pay attention to Mr Trump's tweets."

Speaker of the House Paul Ryan, who is the Republican Party's highest-ranking elected official, said Thursday he was not yet willing to support Trump after repeatedly seeking to distance himself from the front-runner in recent weeks.

On Friday, Ryan's office said that he and other members of the House Republican leadership would meet next week with Trump to "begin a discussion about the kind of Republican principles and ideas that can win the support of the American people this November."

One of Trump's vanquished rivals for the conservative party's nomination, former Florida governor Jeb Bush, congratulated Trump on winning the nomination, but said Friday he would not vote for him or Democratic front-runner Hillary Clinton.

In a Facebook post, Bush said there was no doubt Trump had tapped into "the deep sense of anger and frustration" so many Americans feel.

He said voters "have made it clear that Washington is broken, but I'm not optimistic that either of the leading candidates for president will put us on a better course."

Bush, who had been expected to be a top Republican contender, said that the presidency demands "great fortitude and humility and the temperament and strong character to deal with the unexpected challenges that will inevitably impact our nation in the next four years."

Trump has not demonstrated that temperament or strength of character, Bush said.

"He has not displayed a respect for the Constitution. And, he is not a consistent conservative. These are all reasons why I cannot support his candidacy."

Bush joins his father and brother in distancing himself from Trump.

Media reports this week suggested that former presidents George Bush (1989-93) and his son, George W Bush (2001-09), had no plans to endorse Trump or attend the Republican nominating convention in Cleveland, Ohio.

Dick Cheney, who served as vice president under George W Bush, told CNN Friday that he would support Trump.

Former Massachusetts governor Mitt Romney, the Republican nominee in 2012 when Obama was re-elected, has likewise spurned Trump. Among the party's living presidential nominees, only former senator Bob Dole, who fell short against Democratic president Bill Clinton in 1996, reportedly plans to attend the convention in July.

Later Friday, a federal judge in San Diego, California, set a trial date of November 28 - less than three weeks after the presidential election - for a class action fraud lawsuit brought against Trump's now shuttered Trump University.

The plaintiffs in the case, one of three similar lawsuits brought against the school, claim they paid up to 35,000 dollars for an education in real estate entrepreneurship only to "quickly find out, all Trump University provides is empty promises."

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