The Indiana primary is on May 3, Oregon's is May 17 and New Mexico's June 7.
Trump, in a series of tweets, blasted the partnership.
Trump has won the most state nominating contests, but he has a tough path to earn the 1,237 delegates needed to secure the nomination. The Cruz and Kasich campaigns believe their agreement to cede states where the other candidate appears strong could help limit Trump's ability to win more delegates.
Some Republican strategists who oppose Trump have been calling for such a deal for weeks. The question for Cruz and Kasich is whether their agreement is too late.
If no candidate has enough support by the first vote at the Republican National Convention in July, many delegates will be allowed to switch sides on subsequent ballots.
Cruz campaign manager Jeff Roe said Trump, who has offended women, Hispanics and other groups with controversial statements, would lose a general election contest against the eventual Democratic nominee in the Nov. 8 election.
"Our goal is to have an open convention in Cleveland, where we are confident a candidate capable of uniting the party and winning in November will emerge as the nominee," Kasich chief strategist John Weaver said in a statement.