Madagascar's embattled President Andry Rajoelina said on Monday he was sheltering in a "safe place" following an attempt on his life, ignoring calls to resign after spiralling unrest that has forced him into hiding.

The twice-delayed speech marked his first public address since a mutinous army unit backed anti-government protests, and followed reports that the 51-year-old leader had fled the country.

"Since September 25, there have been attempts on my life and coup attempts. A group of military personnel and politicians planned to assassinate me," he said in a live address on Facebook.

"I was forced to find a safe place to protect my life," he said, without revealing his location.

The protests, led by mostly young demonstrators, erupted over chronic power and water cuts in the impoverished Indian Ocean country, but developed into a broader anti-government movement calling for Rajoelina to resign.

Rajoelina, a former mayor of the capital, Antananarivo, called for the constitution to be respected, ignoring calls to step down.

"I am on a mission to find solutions," he said.

Rajoelina first came to power in 2009 following a coup sparked by an uprising that ousted former president Marc Ravalomanana.

Radio France Internationale said Rajoelina left Madagascar on a French military plane at the weekend, but French officials have refused to confirm or deny this.

French President Emmanuel Macron, who expressed "great concern" over the island's crisis, also refused to confirm this.

Rajoelina has not appeared in public since Wednesday and his address, set for state television and radio, was twice delayed on Monday as armed forces attempted to seize the state broadcaster. (AFP)