The protests, inspired by Gen Z-led movements in Kenya and Nepal, began on September 25 over water and electricity shortages but have since escalated, posing the most serious challenge to President Andry Rajoelina's rule since his re-election in 2023.
Earlier on Saturday, some troops from the elite CAPSAT unit that helped Rajoelina seize power in a 2009 coup urged fellow soldiers to disobey orders and back the youth-led protests.
Prime Minister Ruphin Fortunat Zafisambo, speaking on the state-run TVM channel late on Saturday, said the government was "fully ready to listen and engage in dialogue with all factions - youth, unions, or the military".
Rajoelina appointed Zafisambo and a new defence and security minister after dissolving the previous government last week in response to the protests.
But the moves have failed to assuage public anger.
Videos circulating on social media on Saturday showed CAPSAT soldiers urging fellow troops to "support the people".
A video broadcast by local media showed that dozens of soldiers left the barracks to escort thousands of protesters into May 13 Square, the scene of many political uprisings, which had been heavily guarded and off limits during the unrest.
The army's chief of staff, General Jocelyn Rakotoson, later made a statement broadcast on local media urging citizens to "assist the security forces in restoring order through dialogue".
The demonstrators are demanding that Rajoelina step down, apologise to the country and dissolve the Senate and electoral commission.
Late on Saturday, the presidency released a statement in response to what it called "the spread of false information on social media," following widespread speculation that Rajoelina, who also has French citizenship, had fled the country.
"It is hereby made known to everyone that the president of the republic is in the country and is overseeing the management of national affairs together with the prime minister, head of government," the statement said.
At least 22 people have been killed and 100 injured in the unrest, according to the United Nations.
The government has disputed the figures, with Rajoelina saying this week that 12 people were killed in the protests.
