Meg Whitman, the head of technology firm Hewlett Packard Enterprise Co., said on Sunday that Donald Trump was "unfit" for the U.S. presidency, and criticized New Jersey Governor Chris Christie, whose failed presidential bid she supported, for endorsing him.

But, later in the day, Trump picked up another high-profile endorsement, from U.S. Senator Jeff Sessions of Alabama, a leading conservative.

Trump's insurgent campaign has riven the Republican Party, with party leaders openly discussing how to thwart the will of the tens of thousands of members who have voted for Trump, helping him comfortably win in three of the four states that have so far held nominating contests.

Party leaders are nervous that Trump, a billionaire real-estate developer from New York City who deviates from some of the central tenets of Republican conservatism, may alienate voters if he is their candidate in the Nov. 8 general election. He has proposed banning Muslims from entering the United States and declined a journalist's invitation on Sunday to condemn the Ku Klux Klan, the violent white-supremacist group.

Christie, who scrapped his own presidential bid earlier this month, became the most prominent Republican figure to break ranks with party leadership by endorsing Trump on Friday ahead of this week's "Super Tuesday" contests, when voters in 11 states go to the polls.

Whitman, who was a co-chairwoman of the national finance committee of Christie's campaign, said in a statement to reporters that Trump would take the country on "a dangerous journey" and that Christie was aware of this.

"Chris Christie's endorsement of Donald Trump is an astonishing display of political opportunism. Donald Trump is unfit to be president", said the statement from Whitman, who is chief executive and president of Hewlett Packard Enterprise and chairman of HP Inc <HPQ.N>.

She called on Christie's donors not to follow him to Trump, who has predominantly funded his campaign with personal loans. Representatives of Christie and Trump did not respond to requests for comment.

Earlier on Sunday, Trump was asked repeatedly if he would unequivocally condemn the Klan and other support from white supremacists.

"I don't know anything about what you're even talking about with white supremacy or white supremacists," Trump told CNN's Jake Tapper after being asked about his endorsement by David Duke, a former Klan leader. "If you would send me a list of the groups, I will do research on them and certainly I would disavow if I thought there was something wrong."

Previously, Trump had seemed less uncertain about his views on Duke. "David Duke endorsed me?" he said in a response to a reporter. "Alright. I disavow. OK?"

His latest backer, Senator Sessions, has had to defend his own controversial comments about the Klan in the past. In 1986, he admitted during an unsuccessful confirmation hearing to become a federal judge that he had said he thought the Klan was "OK" until he came to believe that some members smoked marijuana. He explained that these remarks were a joke and has since called the Klan "destestable."

In a separate interview on Sunday, Trump also defended posting on his Twitter account a quote sometimes attributed to Italian fascist leader Benito Mussolini. He told NBC News he did not realize that the quote - "It is better to live one day as a lion than 100 years as a sheep" - was associated Mussolini but said it did not matter because it was a good aphorism all the same.

Many party leaders hope U.S. Senator Marco Rubio of Florida will somehow overtake Trump before the party's nominating convention in July, despite Rubio's not having won any states and lagging behind in Trump in opinion polls.

In recent days, Rubio has taken to adopting Trump's habit of using adolescent insults to denigrate his rival, suggesting on Friday that Trump urinated in his trousers during last week's televised debate.

Rubio and U.S. Senator Ted Cruz of Texas, the only Republican to yet beat Trump in a primary election, both criticized Trump's reticence to speak ill of the Klan on Sunday.

"We cannot be a party that nominates someone who refused to condemn white supremacists and the Ku Klux Klan," Rubio told a crowd of voters in Purcellville, Virginia, MSNBC reported.