1250 GMT November 20, 2019
Senior party activist Jan Halper-Hayes said she thought Trump was "psychologically unbalanced", BBC reported on Wednesday.
In the latest controversy, Trump 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, who are up for reelection in November. Both men have publicly criticized him.
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".
Dozens of senior Republican Party figures have already said they would not vote for Trump, including the party's 2012 nominee Mitt Romney and former Florida Governor Jeb Bush.
Despite the criticism, Trump tweeted on Wednesday that there was "great unity in my campaign, perhaps greater than ever before".
Obama: Trump 'unfit' for presidency
In a searing and virtually unprecedented presidential rebuke, US President Barack Obama declared Trump "unfit" to be president and called on the party leaders to disown him.
Obama piled on as Trump's campaign reeled from multiple self-inflicted scandals, calling the 70-year-old mogul "woefully unprepared" and "unfit to serve as president."
"He keeps proving it," said Obama.
Obama's comments came amid a roiling war of words between Trump and the father of a slain US soldier (Army captain Humayun Khan) who rebuked the Republican nominee as having "sacrificed nothing."
'You want to retch'
French President Francois Hollande also strongly criticized Trump, saying some of the things Trump does make him sick.
"Some excesses make your stomach turn, even in the United States, especially when — as did Donald Trump — he speaks ill of a soldier, of the memory of a soldier," Hollande said according to three people present at a meeting Tuesday with members of the French Presidential Press Association.
Hollande was referring to Trump's comments about Khan.