Media playback is unsupported on your device Media caption Dr Halper-Hayes of Republicans Overseas says Donald Trump is "out of control"

Fresh divisions are emerging within the US Republican Party over its presidential candidate Donald Trump.

Republican donor Meg Whitman has endorsed his rival Hillary Clinton, saying Mr Trump's "demagoguery" had undermined the national fabric.

Senior party activist Jan Halper-Hayes told the BBC she thought Mr Trump was "psychologically unbalanced".

In the latest controversy, Mr Trump has refused to support two senior figures in his own party.

In an interview for the Washington Post, he said he was "just not quite there yet" when asked if he would endorse House Speaker Paul Ryan and Senator John McCain. Both men, among the most senior elected Republicans in the country, face primary votes after challenges from within their own party ahead of their re-election bids in November.

The two had both criticised Mr Trump's attacks on the bereaved parents of a US Muslim soldier killed in Iraq, but have both endorsed him for the presidency.

The Republican presidential nominee's ongoing war of words with the parents of Capt Humayun Khan has intensified rifts within the party.

US media report that Mr Trump has ignored pleas from his own advisers and senior Republican figures to end the feud with the Khan family.

President Barack Obama has questioned why the Republicans have not disowned Mr Trump, saying the billionaire does not have the judgement or temperament to occupy the White House.

Ms Whitman, writing on Facebook, said that to vote Republican out of party loyalty alone "would be to endorse a candidacy that I believe has exploited anger, grievance, xenophobia and racial division".

"Trump's unsteady hand would endanger our prosperity and national security. His authoritarian character could threaten much more," the Hewlett-Packard executive said.

Image copyright AFP Image caption Khizr Khan, whose son Capt Humayun Khan died in Iraq, criticised Mr Trump at the Democratic National Convention

Dr Halper-Hayes, vice-president of Republicans Overseas Worldwide, told the BBC's Today programme that she was "very concerned" about Mr Trump's behaviour, although she would not go so far as to endorse Mrs Clinton.

"I think there is an element of him that truly is psychologically unbalanced, and I feel very guilty for saying this because I'm a Republican and I want the Republican ticket to win," she said.

"But Donald is out of control right now and he's not listening to anyone."

Political calculus - analysis by Anthony Zurcher, BBC News North America reporter

The Donald Trump roller-coaster is picking up speed.

Thanks to a week with enough controversies for an entire election season, Republicans are flooding the media with reports of campaign chaos and an impending mass defection from their nominee if things don't turn around quickly.

Behind all these stories of political discord, however, is the simple fact that while insider establishment operatives may be looking for the exits, Republican officeholders who must eventually answer to the 13 million Trump primary voters have yet to break ranks.

Things will have to get very bad - much worse than they are now - to result in the sort of doomsday scenarios currently being pondered.

It is a simple political calculus. The key, as always, is in the polls and public sentiment.

If Mr Trump appears to have a reasonable chance to win in November, he will persevere, as he has all year.

If his poll numbers crash, and Republican politicians start worrying more about losing their own races in November than alienating their party's base, the Trump-coaster could career off the rails at last.

Going against Mr Trump is still a risky bet. And when it comes to preserving their jobs, politicians are all about minimising risk.

Read more from Anthony

Dozens of senior Republican Party figures have already said they would not vote for Mr Trump, including the party's 2012 nominee Mitt Romney and former Florida Governor Jeb Bush.

New York Representative Richard Hanna became the first Republican member of Congress to publicly say he would vote for Mrs Clinton. He described Mr Trump as "deeply flawed in endless ways".

On Monday, Sally Bradshaw, a top adviser to Jeb Bush, said that Mr Trump's candidacy had convinced her to leave the Republican Party.

Many Republicans opposed to Mr Trump have stopped short of supporting Mrs Clinton, saying they would vote for a third candidate instead.

However, former Republican congressman John LeBoutillier told the BBC's Newsday programme he believed many Republican politicians would back Mrs Clinton.

"Now I think in private a lot of Republican congressmen are going to vote for Hillary, they can't stand Trump," he said.

Despite the criticism, Mr Trump tweeted on Wednesday that there was "great unity in my campaign, perhaps greater than ever before".

Media playback is unsupported on your device Media caption Donald Trump asks a woman with a crying baby to leave a rally in Virginia

Mr Trump's son Eric defended his father's comments about the Khans, telling CBS News that they had been been "blown hugely out of proportion".

In response to Mr Obama's criticism, Mr Trump dismissed the president's time in the White House as a "disaster".

"He's been weak, he's been ineffective... the worst president, maybe, in the history of our country", he said in a Fox News interview.

Mr Trump's spokeswoman Katrina Pierson later caused a social media storm by blaming both President Obama and Mrs Clinton for the death of Capt Humayun Khan, citing their policies on Iraq. Capt Khan died in 2004 when Mrs Clinton was in the US Senate and five years before Mr Obama became president.

Mr Trump drew further ire from veterans' groups on Tuesday for his response when he was handed a Purple Heart - a medal given to wounded members of the US military - at campaign rally in Virginia.

"I always wanted to get the Purple Heart," he said. "This was much easier."

Mr Trump, 70, avoided being drafted to fight in Vietnam as he received five deferments - four for study, and one for heel spurs.

Mrs Clinton has been actively courting moderate Republicans. A Reuters/Ipsos opinion poll suggested she had extended her lead over Mr Trump to eight percentage points, from six points on Friday.

Republicans not voting for Mr Trump

Barbara Bush, former first lady

Jeb Bush, former Florida governor, 2016 presidential candidate

William Cohen, former secretary of defence

Jeff Flake, Arizona senator

Lindsey Graham, South Carolina senator, 2016 presidential candidate

Larry Hogan, Maryland governor

John Kasich, Ohio governor, 2016 presidential candidate

Mark Kirk, Illinois senator

Mitt Romney, former Massachusetts governor, 2012 Republican presidential nominee

Ileana Ros-Lehtinen, Florida congresswoman

Ben Sasse, Nebraska senator

Republicans voting for Mrs Clinton