Several opposition groups announced plans to march Monday in the residential neighborhood of Petion-ville, just to the east of the capital, Port-au-Prince, considered a presidential stronghold.
The same day, supporters of Martelly plan to hold demonstrations in the capital.
Opposition protests are also planned in other Haitian cities, including Cap-Haitien, the country's second biggest city, despite an appeal for calm from the president.
"We are going to take precautions with our meager resources to ensure security, but we ask demonstration organizers to work with police to avoid any violence," a police spokesman said.
More From This Section
"Such crimes are particularly disturbing as they endanger the safety of all, and the social peace that Haiti needs to move forward on the path of strengthening Rule of Law and socio-economic development," a top UN official in Haiti, Sandra Honore, said in the statement.
Haiti, the poorest country in the Americas, has seen a wave of anti-government demonstrations over the past month, with protesters accusing Martelly of failing to ease poverty and unemployment and demanding his resignation.
A Haitian lawmaker has accused both sides of distributing weapons to their supporters in Cite-Soleil, the capital's biggest slum, where more than 40 people were shot dead in recent days in clashes between rival bands.
Martelly has appealed for calm and warned that protests for his resignation "won't help Haiti move forward.