Martelly had been expected to address the issue in a speech to the nation Friday evening, but he canceled his address without giving a reason. Martelly's office did not immediately respond to a request for comment.
Government opponents have insisted that the first round of presidential balloting on Oct. 25 was marred by massive fraud in favor of the president's handpicked successor, businessman Jovenel Moise. The runoff was originally supposed to be held Dec. 27, then rescheduled for Sunday.
Jude Celestin, also a businessman and the other candidate in the runoff, said he would boycott the vote, though his name remained on the ballot.
Neither candidate immediately returned messages seeking response to the electoral council's decision.
Protests have grown increasingly violent in recent days, prompting the council to conclude it was too risky to try to hold the vote. Haiti has only a shaky handle on security even with the assistance of troops and police from a U.N. peacekeeping force that has been in the country since a 2004 uprising ousted then-President Jean-Bertrand Aristide.
Electoral Council offices in various towns have been attacked and set on fire in recent days, and election materials in a remote part of the country were hijacked by gunmen, Opont said.
Recent opposition-stoked protests in Port-au-Prince have ramped up the tension with rock-throwing partisans and burning street barricades.
Several thousand demonstrators cheered in celebration Friday after hearing the vote would be postponed. Groups of mostly young men then proceeded to Petionville, a hillside district that is home to some of Haiti's wealthiest citizens, where they smashed car windows, set a few vehicles alight and hurled rocks at police.
There has been growing concern that a flawed runoff might push the perennially volatile country of 10 million people to the edge of tumult, rolling back a decade of relative political stability and putting the brakes on foreign investment.
Elections are always a struggle in Haiti. It saw its first genuinely democratic election in 1990, closely followed by a coup d'etat. While there have been no shortage of opposition boycotts since, this is the first time that a presidential candidate is boycotting a runoff after qualifying for it.
Celestin recently told The Associated Press that Haiti was "moving toward a selection, not an election."
Haiti's Senate and various religious, business and civil-society groups had called for a halt to Sunday's runoff due to public suspicion of fraud and meddling by the U.S. and other foreign governments.
Martelly had said the runoff would go on as scheduled and accused the opposition of trying to derail the vote with bogus accusations so a transitional government they would dominate could be set up.
Haitian observer groups, who sent over 1,000 people to polling stations in October, had announced that they would not monitor the runoff.
The Associated Press