But that afternoon, Mr. Cruz came upon Mr. Clinton at the airport, where both men happened to have landed for events for the respective campaigns.

Angel Urena, a spokesman for Mr. Clinton, and Catherine Frazier, a spokesman for Mr. Cruz, both confirmed the encounter, but declined to discuss any details of what happened or what they discussed.

But according to three people briefed on the interaction, who were granted anonymity to describe the meeting, Mr. Cruz had landed at the airport before Mr. Clinton did, for an event tucked into his schedule just a day earlier. The Secret Service traveling with Mr. Clinton established that Mr. Cruz was on the other plane with a small coterie of aides; when Mr. Cruz learned that the former president was there, he expressed interest in saying hello, according to the people briefed on the encounter.

The visit, in many ways, was a vintage performance for Mr. Clinton, who as president made a point of attempting to charm political rivals. That is not an approach that Mr. Cruz has taken since becoming a senator, although his rise in politics was fueled in part by personal relationships with members of a Washington establishment that he publicly disparages.

Still, Mr. Clinton, without staffers by his side, joined Mr. Cruz and three aides, according to the people briefed on the encounter.