SAN JUAN, P.R. — Facing an angry public uprising against his administration, Gov. Ricardo A. Rosselló of Puerto Rico announced on Sunday evening that he would not seek re-election in 2020, and would step down as president of his political party.

But Mr. Rosselló did not resign the governorship, as tens of thousands of Puerto Ricans have demanded.

“I am aware of the dissatisfaction and discomfort you have,” Mr. Rosselló said in a brief address on Facebook Live. “I have heard you, and I hear you today. I have made mistakes, and I have apologized.”

“All of my time must be dedicated to the responsibilities that I took on as governor,” he added.

Far from quelling the furor that has led to more than a week of mass protests in San Juan, the governor’s announcement seemed to have the opposite effect: People quickly gathered on the street outside the governor’s official residence in the Old San Juan neighborhood and said they were even more determined than ever to oust him.