Kasich, who lost in the Republican primary to Trump, is not expected to attend the GOP convention in Cleveland. He has not endorsed Trump, the party's presumptive nominee.
Calling into "The O'Reilly Factor" as the first night of the convention kicked off, Trump said he did not consider Kasich a sore loser.
"He lost very very badly and maybe if I were in his position I wouldn't show up either," Trump said of Kasich, noting that he signed a pledge to support the eventual nominee.
Kasich, who is still popular in Ohio, is considered a more mainstream Republican than Trump and struck a more optimistic tone in the primaries. In the GOP primary, Kasich won only Ohio, a key swing state in the general election.
He spoke at the NAACP convention in Cincinnati on Sunday, which Trump declined to attend, and will appear at other events this week. Trump contended Kasich should "at least show up and say hello" at the GOP convention.