By Alana Wise and Jeff Mason

WASHINGTON (Reuters) - U.S. presidential nominee Donald Trump ratcheted up tensions in his Republican Party on Tuesday, denying leading figures support in their re-election bids, while his Democratic rival Hillary Clinton won her first endorsement from a Republican lawmaker.

President Barack Obama blasted Trump as unfit to be president and questioned why any Republican would support the New York businessman seeking his first public office.

"The question I think that they have to ask themselves is, if you are repeatedly having to say in very strong terms that what he has said is unacceptable: Why are you still endorsing him?" Obama, a Democrat, said at a White House news conference with Singapore's prime minister, Lee Hsien Loong.

Trump, a former reality TV star, has troubled many in the Republican establishment with his off-the-cuff, often insulting style, and controversial policies including a proposed ban on the entry of Muslims to the United States and his plan to build a wall along the Mexican border to keep out illegal immigrants.

The latest exchanges cast a shadow over the show of unity the party sought to project at the Republican National Convention that formally nominated Trump for president in July.

Interviewed by The Washington Post, Trump said he could endorse neither House Speaker Paul Ryan nor Senator John McCain, both of whom face Republican challengers in primary votes in their states ahead of the Nov. 8 general election.

Both lawmakers had rebuked Trump over his feud with the family of a slain Muslim-American Army Captain Humayun Khan.

Mirroring the language Ryan used about supporting Trump before his eventual endorsement, Trump told the newspaper he was "not quite there yet" in endorsing Ryan, the highest ranking elected Republican, in next Tuesday's Wisconsin primary.

Trump praised Ryan's opponent, Paul Nehlen, for running “a very good campaign.” Trump said Ryan had sought his endorsement, but that as of now he is only “giving it very serious consideration.”

HANNA ABANDONS TRUMP

Although several Republicans in Congress have said they will not support Trump, Representative Richard Hanna of New York was the first to take the extra step and endorse Secretary of State Clinton, the Democratic nominee.

Hanna, who is retiring from the House of Representatives rather than seek re-election, said his decision was prompted by Trump's attacks on the parents of Captain Khan, who was killed in the line of duty in Iraq in 2004.

The Republican lawmaker called Trump "deeply flawed in endless ways," "unrepentant" and "self-involved."

"For me, it is not enough to simply denounce his comments: He is unfit to serve our party and cannot lead this country," Hanna wrote in a letter posted on syracuse.com, the website of the Post-Standard newspaper in New York.

Hanna's retirement gives him the leeway to risk upsetting colleagues and voters. Senator Ben Sasse of Nebraska, one of the most outspoken Trump critics in Congress, said he would never join Hanna in voting for Clinton.

Trump has had a running feud with Khizr and Ghazala Khan since they took the stage at last week's Democratic convention to cite their son's sacrifice and criticize Trump's proposed ban on Muslims.

The uproar has led many Republicans to distance themselves from the New York businessman and voice support for the Khan family.

Obama said Trump's attacks on the Khans showed he was "woefully unprepared" to be president.

Republican Chris Christie, a Trump ally once viewed by Trump as a potential running mate, joined the fray on Tuesday, calling criticisms of the Khan family "inappropriate."

Ryan and Republican Senate Majority Leader McConnell have offered support to the Khans, but no Republican leaders have withdrawn their support for Trump as the party's presidential pick.

'HUGELY OUT OF PROPORTION'

Trump's son, Eric Trump, told CBS News on Tuesday his father's comments toward the Khans have been "blown hugely out of proportion."

    Trump has fallen behind Clinton in opinion polls made public since the parties held their nominating conventions last month.

Clinton extended her lead over Trump to eight percentage points, according to a Reuters/Ipsos poll released on Tuesday, from six points on Friday. About 43 percent of likely voters favor Clinton, 35 percent favor Trump, and 9 percent picked "Other."

Trump also has trailed Clinton in fundraising. The Democrat reported raising nearly $90 million in July for her campaign and the Democratic Party, with more than half the donations coming from new donors.

Interviewed on the Fox Business television network, Trump brushed off billionaire investor Warren Buffett's blistering critique of his business acumen.

Buffett, chairman and chief executive officer of Berkshire Hathaway Inc BRKa.N, scorned Trump's 1995 move to list Trump hotels and casino resorts on the New York Stock Exchange, saying it lost money for the next decade and that a monkey would have outperformed Trump's company.

Trump, who has said his business success qualifies him to lead the country, defended his record running his hotel and casino business in Atlantic City, New Jersey.

"I had great timing. I got out," after seven years, he told the network on Tuesday. "I took a lot of money out of Atlantic City, which is what I'm supposed to do. I'm a businessperson."

(Additional reporting by David Morgan, Susan Cornwell, John Whitesides and Doina Chiacu; Writing by Caren Bohan; Editing by Frances Kerry and Howard Goller)