Rosselló's announcement on Sunday that he would not seek re-election next year and would step down as head of the New Progressive Party failed to appease the crowds, who called for him to immediately surrender the governorship.
The island’s largest newspaper called on the first-term governor to leave office and reported over 500,000 protesters took to the streets in San Juan.
Reuters was not able to verify the crowd size and police were not immediately available for comment.
President Donald Trump also blasted the 40-year-old governor, who is affiliated with the U.S. Democratic Party.
"He's a terrible governor," Trump said at the White House on Monday, after feuding with Rosselló in 2017 over the speed and scale of the federal response to Hurricane Maria. "You have totally grossly incompetent leadership at the top of Puerto Rico."
In San Juan, demonstrators dressed in black T-shirts filled the city's largest highway and marched in the pouring rain with celebrities like Ricky Martin and Reggaeton star Daddy Yankee in the tenth day of sometimes violent protests.
"In Puerto Rico we don't follow dictators. It's time for you to go," a drenched Martin, 47, the target of homophobic messages in Rossello's chats, told cheering crowds.
"Despacito" singer Daddy Yankee was among protesters who headed to San Juan's old city where they demonstrated in front of police and orange plastic barriers near the governor’s official residence, a mansion known as "The Fortress."
As crowds chanted "Ricky Resign!" television images showed some protesters carrying machetes with the Puerto Rican flag painted on them.
San Juan Mayor Carmen Yulin Cruz, an opposition politician running for governor in 2020, said Rosselló had run out of time.
"The country can't put up with anymore of this," Yulin Cruz said in a video posted from the march, wearing a black T-shirt with the message "The power is in the street."
Rosselló on Monday again asked Puerto Ricans to give him another chance.
“I used words that I apologised for but I've also taken significant actions in the direction of helping vulnerable sectors,” Rosselló told Fox News, explaining he had made policy changes significant to women and the LGBTQ community.
Those two groups were frequent targets of misogynistic and homophobic messages exchanged between Rosselló and top aides in 889 pages of online group chats published July 13 by Puerto Rico's Center for Investigative Journalism.
The crass messages showed a political elite intent on maintaining power on an island where people still live under blue tarpaulins two years after hurricanes ripped roofs off their homes and killed over 3,000 people.
Protests have brought together Puerto Ricans from different political parties, and non-political islanders to vent anger at alleged corruption in the administration and its handling of hurricane recovery efforts.
Puerto Rico's nonvoting representative to the U.S. Congress Jenniffer González, seen as a possible candidate for governor, as well as a string of Democratic presidential candidates and lawmakers have called for Rosselló to step aside.
Puerto Rico House Speaker Carlos Mendez, part of Rosselló’s New Progressive Party, appointed an independent panel on Friday to investigate whether the chats warranted impeachment.
The political turmoil comes at a critical stage in the island's bankruptcy as it tries to restructure some $120 billion in debt and pension obligations.
It has also raised concerns among U.S. lawmakers who are weighing the island's requests for billions of federal dollars for healthcare and work to recover from Hurricane Maria.