"They want to make sure they pick somebody who can win in the fall," Kasich said Wednesday on CNN's "Erin Burnett OutFront." "If we pick these two guys, according to virtually all the polls, we are going to get creamed."
Kasich was referring to his primary opponents: Texas Sen. Ted Cruz and GOP front-runner Donald Trump.
Republican National Committee members gathered in Florida this week as the focus on the party's nominating convention intensifies. Each of the GOP campaigns were set to make their own pitches at the gathering, with Kasich and Cruz making theirs personally.
Following Trump's win in New York, Cruz has joined Kasich in being mathematically eliminated
from securing the nomination ahead of the convention, a CNN analysis shows.
In response to comments from Cruz earlier in the day that Kasich "has no path whatsoever to the nomination," the Ohio governor said, "If he's so sure of that, why is he attacking me all of the time?"
Kasich has staked a position based on a positive tone and an appeal to moderates.
"I don't think the Republicans want to pick somebody who has no appeal to independents and no appeal to conservative Democrats. That's what my appeal is," Kasich said.
Kasich also touted his performance in the New York primary relative to Cruz, calling the Texas senator's gain's "pretty anemic."
As for his own performance in the New York contest, Kasich quipped, "I won Manhattan. Maybe I can go for mayor."