Story highlights Kasich hasn't decided whether he can endorse Trump

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

Washington (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."

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