Photo Newspapers for sale in Abidjan, Ivory Coast, on Friday featured front-page articles about the turmoil in neighboring Burkina Faso. Credit Sia Kambou/Agence France-Presse — Getty Images
OUAGADOUGOU, Burkina Faso — After violent protests in which demonstrators set Parliament on fire and surged through the streets of the capital in a wave of dissent, President Blaise Compaoré of Burkina Faso said he had “heard the message, understood it and taken note of the strong desire for change.”

But in a statement late Thursday, Mr. Compaoré said he would not heed protesters’ demands for his immediate resignation, instead offering negotiations on “a transitional period at the end of which I will hand over power to the democratically elected president.”

He also rescinded a declaration of martial law, made only hours earlier, and abandoned plans to change the Constitution in order to permit him to extend his 27-year tenure in this impoverished West African nation.

Opposition to the president’s plans for another term had been building for weeks. Anger exploded Thursday as protesters stormed the Parliament building, bursting past police lines to prevent lawmakers from voting on a draft law that would have allowed Mr. Compaoré to run again next year.

It was unclear early on Friday whether the president’s offer of negotiations would avert another day of protests representing the most serious challenge to his authority since he seized power in a military coup in 1987.

Hundreds of protesters gathered in central Ouagadougou, the capital, on Friday, and the opposition promised to offer its response to the president’s move at a news conference.

A day earlier, thousands rampaged through Ouagadougou, burning the homes of presidential aides and relatives and looting state broadcasting facilities. Social media sites showed images of demonstrators toppling a statue of Mr. Compaoré.

The violence set off a series of decrees from the embattled president, who declared martial law, permitting the military to suspend both the Parliament and the government, and to inaugurate a 12-month transition to elections under an interim government.

Opposition leaders called his actions a coup.

In his statement late Thursday, Mr. Compaoré, a former army officer who ranks among Africa’s longest-serving leaders, said that the government would remain “dissolved,” but that martial law would be “canceled.”