However, the campaign is also calling on the #NeverTrump movement to come to its aide.
In new digital videos from Kasich's campaign, as well as a similar TV ad from the super PAC supporting him, Cruz's comments disparaging "New York values" are highlighted.
And in a new TV ad, first reported by The New York Times, Kasich's campaign says Cruz won't be able to defeat Democratic candidate Hillary Clinton in the general election.
In a fundraising email sent to supporters Thursday night, campaign manager Beth Hansen highlights the TV ad ahead of the April 19 primary.
"Don't be fooled. Ted Cruz can't win the nomination outright," says the TV ad slated to start playing Friday in New York City and Long Island, as well as upstate New York.
"You have only one choice. One choice that will stop the Clinton political machine. John Kasich," the voiceover states.
Eyeing delegates in congressional districts
New York's delegates are awarded proportionally. Kasich is hoping to pick up delegates in congressional districts across the state that will help him in a contested convention.
"If the Never Trump movement is serious about its mission to stop Donald Trump, then it will go all out to keep him under 50% statewide and in congressional districts and make the same effort for John Kasich in New York as it did for Ted Cruz in Wisconsin," campaign spokesperson Mike Schrimpf told CNN in a statement.
"The fact is while Ted Cruz disparages New York values, John Kasich is Donald Trump's main competition in the state," Schrimpf's statement reads.
It is a message that Kasich has been pushing on the campaign trail, saying Cruz's first place win in Wisconsin, and his own last place finish, was more a product of the anti-Trump movement than "pro-Ted Cruz votes."
"We're now getting to the place where we feel we have the best chance of being able to accumulate delegates," Kasich said, looking ahead to New York's election as well as elections in Maryland and Pennsylvania.
The most recent public poll of New York voters, from Monmouth University, has Trump at 52%, Kasich at 25% and Cruz at 17%.