Madagascar's President Andry Rajoelina said he planned to hold a "national dialogue" with various groups on Wednesday after youth protesters issued a 48-hour ultimatum for him to agree to their demands or face a national strike.

On Monday, Rajoelina named army General Ruphin Fortunat Zafisambo as the new prime minister a week after he fired his cabinet in a move intended to address some of the grievances that sparked the demonstrations on September 25.

But the reshuffle has failed to placate the protesters who initially took to the streets over water and electricity shortages in the impoverished African nation but have since expanded their demands to call for Rajoelina's resignation.

Inspired by similar "Gen Z" marches in Kenya and Nepal, the protests are the largest wave of unrest on the Indian Ocean island nation in recent years, giving voice to discontent over rampant poverty and high-level corruption. 

"Together, we must unite to fight against these evils and to build a new society founded on solidarity and mutual respect," Rajoelina said in a message on Tuesday on his office's Facebook page.

"To that end, a national dialogue and consultation will be held to listen to people's concerns and to develop lasting solutions to the issues that affect us."

He said that the talks scheduled on Wednesday afternoon would be attended by spiritual leaders, students, youth representatives, and others.

The protesters did not specify their demands, but in the past they have called for Rajoelina to leave office, apologise to the nation, and dissolve the senate and the election commission.

On Tuesday, dozens of protesters marched in the capital before police dispersed them, privately owned digital news platform 2424.MG reported - a sharp drop from previous demonstrations, which have seen hundreds gather in cities across Madagascar.

The United Nations says at least 22 people have so far died in the protests while 100 others have been injured. The government has rejected the figures.

In a statement posted on the protest movement's verified Facebook page, the demonstrators also rejected the appointment of the new prime minister and described it as a "cosmetic manoeuvre."