Rossello in a Sunday video statement on his Facebook page said he would not run for re-election and would step down as the head of his New Progressive Party.
Offensive messages were found among almost 900 pages of chats from Rossello’s Telegram messenger obtained by Puerto Rico’s Centre for Investigative Journalism. The leaked chats reportedly revealed disparaging remarks by Rossello, including homophobic and misogynistic comments about political rivals.
Thousands of Puerto Ricans earlier this week took to the streets of San Juan demanding Rossello's resignation. Despite clashes and violent protests, Rossello earlier refused to step down.
Some celebrities, including singer Ricky Martin, have arrived in the city in support of the protesters.
Puerto Rico’s Department of Justice has issued a summons for all those involved in the leaks of the offensive chat messages between Rossello and his associates.
US President Donald Trump on Thursday claimed that the scandal reflects on a corrupt Puerto Rican leadership who, according to him, robbed the US government by squandering $92 billion in relief after Hurricanes Maria and Irma.