Republicans mounting a long-shot bid to unseat Senator Kirsten Gillibrand of New York selected Mike Sapraicone, a wealthy private security executive, as their preferred nominee at a party convention on Thursday.

Mr. Sapraicone, 67, has fashioned himself as an affable moderate, vowing to outwork Ms. Gillibrand and find solutions to the migrant and affordability crises that the state’s ruling Democrats have struggled to combat.

“It’s about time we had a voice in New York we haven’t had,” he said in an interview, accusing Ms. Gillibrand of having not been “seen or heard” since her unsuccessful run for president in 2020.

The message easily won over the state’s political establishment, which believes Mr. Sapraicone represents Republicans’ best chance to compete in New York. Eighty-four percent of delegates voted in his favor on Thursday at the convention in Binghamton.

But the show of support apparently failed to clear his path. Rather than drop out, two conservative Republican runners-up, Josh Eisen and Cara Castronuova, signaled their intent to petition onto the ballot and allow primary voters to have the final say in June.

That would set up a potentially messy fight that could expose the deep ideological fissures dividing the party. It threatens to force Mr. Sapraicone not only to tap his campaign treasury but also to adopt more conservative positions on subjects like abortion and former President Donald J. Trump that could hurt the party in November.