"He didn't have the signatures. Does anyone know that?" Trump asked during a rally in Cincinnati on Sunday afternoon.
"So if he doesn't qualify in Pennsylvania, he shouldn't be running on Tuesday. ... That's his problem. Hopefully we can just beat him. Who cares if he qualifies in Pennsylvania?"
Trump also tweeted that because the governor didn't qualify for the ballot, he shouldn't be allowed to participate in Tuesday's Ohio primary.
Kasich said on ABC's "This Week" Sunday morning he will be competing in Pennsylvania, adding that "this will all be resolved soon."
Trump and Kasich are in a close battle for victory Tuesday in Ohio, a winner-take-all state worth 66 delegates. According to the RealClearPolitics average of polls
there, the governor leads Trump by 2 points, 35.3 percent to 33.3 percent.
During the rally Sunday, Trump continued to slam Kasich. He said Ohio has plenty of problems, noting the state's real estate taxes are "through the roof."
"You know what they did is they tried not to raise taxes, but they raised everybody's real estate taxes, so the tax increase is absolutely a disaster," he said.
"And your governor, as you know, voted when he was a congressman, voted for [the North American Free Trade Agreement], which is absolutely, Ohio has never ever come back from that."
He also hit on Kasich for putting on a "nice routine."
"But he didn't start out that way," Trump said.
In the first two debates, Trump said Kasich came at him "viciously."
In the past several debates though, Kasich has been touting that he's the grownup in the room.
"He was vicious, which is OK, he's a governor, he's supposed to be a little bit vicious," Trump said.
"But now he's playing the good guy."
"Interestingly, we have a lot of young people," Trump responded. "We have so many young people at these rallies it's incredible."
But Trump said he would have to look at the decision to determine whether he agrees with it.
Last week, an Ohio judge granted
teenagers who will turn 18 before Election Day the right to vote in the state's presidential primary. Husted bashed the ruling in a statement released following the decision, saying the "last minute legislating from the bench on election day has to stop."
"We will appeal this decision because if there is a close election on Tuesday we need clarity from the Supreme Court to make sure that ineligible voters don't determine the outcome of an election," he said in the statement.