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Story highlights

Kasich hasn't decided whether he can endorse Trump

"I'm not gonna do that," Kasich said of a third party bid

Watch the full exclusive interview with Ohio Gov. John Kasich on “Anderson Cooper 360” at 8 p.m. ET on CNN.

(CNN) —  

John Kasich signaled Monday that he still harbors deep uneasiness with Donald Trump as the Republican nominee, declining to endorse him and reiterating that he will not serve as Trump’s vice president.

Even now that he’s left the race, Kasich is resisting calls to serve as Trump’s No. 2, portraying his pitch and Trump’s as fundamentally incompatible. Kasich said he was “not inclined” to run with Trump and that he had “not changed my mind.”

“Those are two very inconsistent messages, so it would be very hard for me – unless he were to change all of his views and become a uniter – for me to get in the middle of this thing,” the Ohio governor told CNN’s Anderson Cooper in an exclusive interview, his first since leaving the race. “Because, you know, I’m undecided here about what I’m gonna do in this race.”

Kasich maintained that he has not yet decided whether he can support Trump’s message, and further warned that Trump is set to lose in November should he not adopt a more welcoming political posture. Yet he still said Monday that he would not mount a third party bid for the White House, putting an end to budding hopes that the former Republican presidential candidate would reenter the race.

“I’m not gonna do that,” Kasich said. “I gave it my best where I am. I just think running third party doesn’t feel right. I think it’s not constructive.”

Republican elites from across the ideological spectrum have pined for a Trump alternative to run an independent campaign, but Kasich isn’t having any of it. He acknowledged that he has had a phone call with “somebody” who wanted him to mount an independent bid.

“A third party candidacy would be viewed as kind of a silly thing,” he said. “And I don’t think it’s appropriate. I just don’t think it would be the right thing to do.”

Trump’s Indiana GOP primary victory on May 3 prompted both Kasich and fellow GOP primary contender, Ted Cruz, to drop out, making him the presumptive nominee. Yet Kasich is still smarting over the way he believes forces – ranging from top Republican donors to the Republican National Committee – treated him, believing they did not give him a fair shake.

RNC chairman Reince Priebus declared Trump the presumptive nominee on the night of Trump’s Indiana win – even though Kasich had said he was not yet leaving the race.

“.@realDonaldTrump will be presumptive @GOP nominee, we all need to unite and focus on defeating @HillaryClinton #NeverClinton,” Priebus had tweeted.

“The chairman of the Republican Party endorsed Trump, which I thought was completely inappropriate,” Kasich said. “He just wanted to get thing over. I’m not happy about it.”

Kasich also attributed his struggles to his inability to win over many of the party’s leading donors and fundraisers, who largely flocked to other candidates despite his ties to the business community.

“My big problem was I never got the big money. The big money stayed on the sidelines,” he said. “I never had the people walk in and give money to the super PAC.”

But Kasich, like Cruz, is in no rush now to back the man who beat them. The Ohio governor told Cooper that he is still “undecided” about backing Trump, and signaled he would be watching the New Yorker closely and observing his rhetoric.

Kasich, who was far more tolerant of Trump on the campaign trail than were his other GOP rivals, wondered what his daughters would say should he now support him.

“If I were to turn around today and endorse him, they’d be like, ‘Why, Dad?’ And that matters to me,” Kasich said. “We’ll see what he does. He has a chance to move to the positive side and unify this country.”

Kasich predicted that should Trump not change his message to one of unity, presumptive GOP nominee would have a “big problem” in the Buckeye State.