“Many countries are not paying their fair share. That means we are protecting them, giving them military protection,” Mr. Trump told an a crowd of about 650 people at the Racine Civic Center. “They’re ripping off the United States. And you know what we do? Nothing. Either they have to pay up for past deficiencies or they have to get out. And if it breaks up NATO, it breaks up NATO.”

Mr. Trump’s doubts about the necessity of American involvement in NATO, first broached during a meeting with the Washington Post editorial board last month, have become one of an array of flashpoints with Mr. Cruz in recent days.

Mr. Trump said NATO is not capable of defending against terrorism, which he said is more important than providing a hedge against Russia.

“They have to either rejigger it or come up with something new,” Mr. Trump said. “Terrorism is the problem. We have to knock the hell out of these crazy people there.”