SAN JUAN, P.R. — Puerto Rico’s political crisis, which prompted the first resignation of an elected governor in the island’s history, entered a new phase on Thursday as leaders of the ruling New Progressive Party maneuvered to determine who would hold the governorship after Ricardo A. Rosselló steps down.

Eight days before Mr. Rosselló was scheduled to leave the post he has held since 2017, and as public attention shifted from the streets to the corridors of power, no one on the island of 3.2 million people seemed truly certain who the next governor would be.

A series of names have emerged, nearly all of them saddled with political baggage that carries the potential of new popular unrest. Many signs pointed to the likelihood that any new appointee would be selected by Mr. Rosselló — the man many Puerto Ricans fervently wanted out.

The behind-the-scenes scramble portends more complicated days ahead after more than a week of tumultuous street protests and a series of resignations left the government in chaos. Again on Thursday, demonstrators spilled into a highway in San Juan, the capital, and pledged to keep protesting unless the island’s political leaders bring about a genuine change in governance.