"This is not a reality show," Obama tells Trump

Fighting with Obama is a battle Trump would likely relish as he tries to rally support within his own party. During hard-fought Republican primary campaigns, the billionaire delighted in responding to attacks from rivals and found that his support grew when he lashed out at his opponents.

Asked about Trump at a media briefing in the White House, Obama called on the press and public to weigh past statements by the Republican but did not point to any specific issues or remarks.

"This is not entertainment," Obama said, a reference to Trump's television background. "This is not a reality show. This is a contest for the presidency of the United States," he said.

Some top Republican leaders - U.S. House Speaker Paul Ryan among them - are still expressing wariness about Trump, who became the party's presumptive nominee this week when two Republican rivals dropped out of the White House race.

Former Florida Governor Jeb Bush, who ran unsuccessfully for the Republican nomination, posted on Facebook that he will not vote for Trump - one of the sharpest slights yet against the New York real estate mogul by a senior Republican.

"Donald Trump has not demonstrated that temperament or strength of character. 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 wrote, adding that he would not vote for likely Democratic nominee Hillary Clinton either.

U.S. Senator Lindsey Graham from South Carolina, who made an unsuccessful bid for president, joined a growing list of Republicans who are refusing to support Trump and he announced on Friday he will also skip the Republican convention in July. Mitt Romney, who won the Republican nomination in 2012, is also refusing to support Trump.

But Trump on Friday won the endorsement of another former Republican presidential nominee, Bob Dole, who lost to Bill Clinton in 1996.

For Trump, finding unifying enemies like Obama and Hillary Clinton could help rally Republicans back to his side ahead of the Nov. 8 general election.

Obama is likely to be the feature of much of Trump's criticism in the general election. Republicans have sought to paint Clinton as an extension of the Obama administration who would continue all of his policies.

Since effectively securing the nomination on Tuesday, Trump has begun testing themes to attack Clinton, Obama's former secretary of state.

On Friday, Trump took aim at Clinton for her use of a private email server while in office. Clinton has said she did not send or receive information marked as classified. The FBI is investigating whether laws were broken.

"The email scandal should take her down but I don't think it's going to because I think she's being protected by the Democrats," Trump said on "Fox & Friends," a television news program that attracts a large conservative viewership.

CLINTON "BAD ON JOBS"

Trump tried to cast Clinton as weak on the economy, which is sure to be one of the main policy issues as the election approaches.

"If you look at what she's going to do, she's going to be so bad on jobs that wages are going to go down for workers," he said.

Early general election polls show Clinton with a lead both nationally and in key states.

Clinton has a higher probability than Trump of becoming the next president, but the gap between them narrowed this week, according to the online political stock market PredictIt.

A key factor for Trump in the general election will be whether he can rally the party behind him.

Trump has seen some top Republicans who previously fought his candidacy now back him, including Texas Governor Rick Perry. Former Vice President Dick Cheney, whose daughter Liz Cheney is running for Congress in Wyoming, said he will support Trump, a source close to him said on Friday.

Paul Manafort, a top Trump adviser, told MSNBC that Republicans will rally behind the businessman because he has strengthened the party by attracting new supporters.

"We want to unify the party, but the important thing to remember is Donald Trump just won a historic victory among 17 other candidates," Manafort said. "He is a very strong nominee. His vision that he laid out is not something in question."

Republican National Committee Chairman Reince Priebus has already begun his efforts to rally the party behind Trump, saying at an event hosted by Politico that behind the scenes the candidate is "more gracious and personable than I think you see at rallies."

"I think there's work on tone to do," Priebus said, adding that he has made that point to Trump. "I think he gets it. I think you're going to see it. I think you're going to see the change in tone."

In addition to changing tone, Trump also faces an uphill climb to bring the party together. Ryan, the top elected Republican in the United States, said on Thursday he was not ready to support Trump, a sign of lingering establishment concern about the candidate's position on immigration and trade.

Trump took issue with Ryan.

"Paul Ryan said that I inherited something very special, the Republican Party," Trump wrote on Twitter. "Wrong, I didn't inherit it, I won it with millions of voters."

Ryan has invited Trump to meet with House of Representatives Republican leaders next week, Ryan's office said on Friday.

Trump's attorney was quoted in media reports on Friday as saying the candidate will testify after the November election in a class-action lawsuit that accuses him and his now-defunct Trump University of defrauding people who paid up to $35,000 for real estate seminars.

A federal judge ordered the trial in San Diego to start on Nov. 28, which means he will not have to testify while he campaigns. The university case was one of the subjects Trump's rivals used to attack him during presidential debates.