Rosselló, a Democrat and member of the territory's New Progressive Party (PNP), made the announcement Sunday in a four-minute Facebook video. He also said he agreed with the people's right to protest and was willing to confront the impeachment process, which already had begun in Puerto Rico's legislature.
The embattled governor said although he will not resign as the island's leader, he will step down as head of his pro-statehood party.
In the video Rosselló acknowledged his "mistakes" and pointed out that he had apologized in the past. He did not offer a formal apology in Sunday’s video.
Many Puerto Ricans have been calling for Rosselló’s resignation after leaked online chats showed him insulting women and political opponents as well as mocking victims of Hurricane Maria, one of the most devastating natural disasters to hit the island territory.
His official residence has been under siege this week as hundreds of thousands of protesters gathered outside La Fortaleza, the governor’s official residence.
Amid the outcry, the media-friendly governor has avoided public appearances since July 11, making only four brief appearances, breaking from his usual three or four lengthy news conferences in addition to multiple media appearances.
A wave of protests hit the island this past Friday, with union workers marching toward La Fortaleza from the nearby waterfront. Horseback riders and hundreds of other people also joined the march.
Smaller protests also broke out across the island over the weekend, though most people were expected to hit the streets on Monday.
The calls to oust the governor have caught the attention in the mainland U.S. and several officials, including presidential candidate Julián Castro, have come out in support of the protesters.
Castro, a Democrat, openly called on Rosselló to step down, saying "it’s clear that Gov. Rosselló can no longer be effective."
Some well-known athletes with ties to the island also urged the governor to resign last week, including the Los Angeles Dodgers’ Enrique Hernandez and the St. Louis Cardinals’ Yadier Molina.
Puerto Rico’s Center for Investigative Journalism earlier this month published nearly 900 pages of private messages between Rosselló and several other government officials.
In one message Rosselló called one New York female politician of Puerto Rican descent a "w---e" and described another as a "daughter of a b---h." One chat also made vulgar references to Latin pop star Ricky Martin’s homosexuality.
During a July 11 news conference, Rosselló asked Puerto Ricans to forgive him for the comments he made in private. In further media appearances, he continued to ask for forgiveness over the comments many deemed offensive and misogynistic.
Fox News' Mike Arroyo, Lukas Mikelionis and The Associated Press contributed to this report.