“The events of the past two weeks have worsened, even more so over the last six days, paralyzing economic activity and government activity, portraying an anarchic Puerto Rico to the rest of the world,” Ms. González-Colón wrote. “This is not sustainable.”

Puerto Rico’s political parties, which are divided over whether the island should remain a commonwealth, become a state or seek independence, do not match up neatly with those on the mainland. Though they are both New Progressives and support Puerto Rican statehood, Ms. González-Colón is a Republican in national politics, while Mr. Rosselló is a Democrat.

The resignation chorus outside of Puerto Rico has grown to include two New York Democrats: Representative Nydia M. Velázquez, the longest-serving Puerto Rican in Congress, and Representative Alexandria Ocasio-Cortez, who is of Puerto Rican descent and has become an icon for young progressives. Several 2020 Democratic presidential candidates have also said that Mr. Rosselló must go.

On Friday, the Puerto Rican Bar Association released a report outlining the legal grounds for lawmakers to pursue impeachment. El Nuevo Día, Puerto Rico’s largest newspaper, published an editorial accusing legislative leaders of slow-walking impeachment and letting the political crisis continue. The governor’s press secretary, Dennise Pérez, resigned on Friday, saying she drew the line after someone called her “corrupt” in front of her son.

In his address, Mr. Rosselló said demonstrators’ right to free expression would be protected, and he promised to work to regain their trust.

“I recognize that apologizing is not enough,” he said. “Only my work will help restore the confidence of those sectors and get us on the path to true reconciliation.”

Saadi Rosado of the Feminist Collective, a women’s rights group that has been protesting the administration for months, said that while the governor’s announcement may have been intended to defuse the protests planned for Monday, it would actually make things worse for him.