Sen. John McCainJohn McCainA closer look at McCain's proposed defense budget Top Dem comes out against Tillerson ahead of key vote Is McCain confident in Trump? ‘I do not know’ MORE declined on Wednesday to criticize Sarah Palin, his former running mate, for endorsing Republican presidential front-runner Donald TrumpDonald TrumpTrump vows to cut taxes for businesses MSNBC's Halperin: Trump's comments at CIA "most disturbing" Former Clinton spokesman: Virginia elections will begin resistance to Trump MORE.
“I respect her view,” McCain (R-Ariz.) told reporters in the Senate on Wednesday, a day after Palin endorsed the man with whom he has had a bitter feud.
Palin’s decision isn’t affecting his own thinking about the race, McCain added.
“I’m not considering anyone,” he said. “I’ve got my own race to run.”
McCain had previously endorsed Sen. Lindsey Graham (R-S.C.), one of his closest legislative allies. Graham’s campaign never managed to attract sizable support, forcing him to abandon the bid in December.
Trump has criticized McCain’s time as a prisoner of war, saying that he “like[s] people who weren’t captured.”
McCain has fired back with harsh rebukes of his own, claiming that the business mogul's extreme anti-Muslim rhetoric will come back to haunt the United States, and mocking him for receiving praise from Russian President Vladimir Putin.
On Wednesday, he demurred when asked by reporters whether Trump should consider picking Palin as his vice presidential candidate, should he win the GOP nomination.
“That’s up to him, not up to me,” McCain said. “I certainly don’t pretend to know what his thoughts are.”
Others in the Arizona senator's orbit were less guarded about Palin's endorsement on Tuesday evening.
McCain's daughter, Fox News contributor Meghan McCain, said on Fox Business Network on Wednesday that it was “hard for me to watch” the endorsement.
“I wish I just saw this a little less like pandering,” Meghan McCain said. “And doing something that’s popular instead of sticking with your integrity and the kind of conservative beliefs that she has espoused for so long.”
McCain is largely responsible for Palin’s national profile, which he launched by selecting the former Alaska governor to be his running mate in his 2008 campaign against President Obama.
Republican strategist Rick Davis, who served as campaign manager for McCain's 2008 bid, said Wednesday that people are "scratching their head" over Palin's endorsement of Trump.
"I think it's a battle for the dwindling Carson vote," Davis said of the endorsement during an appearance on "CBS This Morning," referring to falling support for Ben Carson. He also noted Trump's speech at Liberty University amid his effort to go after evangelical voters.
The former McCain aide suggested that there wasn't a downside in Iowa of Palin endorsing Trump, but added, "I think in everywhere else in the country, people are scratching their head when they're waking up this morning and saying, 'What is he thinking?'"
Davis said that Trump likely believes that if he can win in Iowa he can move toward a landslide victory.
"You win every day or you lose every day in a campaign at this stage," Davis said. "It was a big win day for Trump and a big lose day for [rival Ted] Cruz."
— Jesse Byrnes contributed.