PORT-AU-PRINCE, Haiti — Volcy Assad, a Haitian political activist, stood before an enormous plume of black smoke emanating from a pile of burning tires and made it clear that the demands of protesters had changed.

“Today we are demanding the departure of Michel Martelly,” Mr. Assad said on Saturday, referring to the Haitian president. Around him, groups of young men, faces covered with T-shirts and bandannas to shield from tear gas, had blocked the streets with rocks.

One day earlier, officials had bowed to widespread civil unrest and postponed a single-candidate presidential runoff vote that was to be held on Sunday. Now, feeling emboldened in their objections to the first round of voting, which many saw as deeply fraudulent, protesters are demanding the ouster of President Martelly. With just two weeks left in office, he has become the central figure in a growing political scandal here that threatens the stability of a nation with a long history of social unrest and turmoil.

Mr. Martelly’s supporters took to the streets on Sunday in counterprotests and vowed to keep him in office, a scenario of competing rallies that experts feared would lead to violence. In Port-au-Prince this weekend, protesters burned cars and barricaded streets as the police responded with water cannons and tear gas.