Myanmar security forces killed at least 14 protesters in the Hlaingthaya district of Yangon on Sunday, the Myanmar Now news service reported, while other domestic media gave higher tolls.
Myanmar Now said the information came from a rescue worker and a hospital near the industrial district.
Yangon-based Thit Khit Media reported 30 civilians were killed in Hlaingthaya.
Daily protests against the military's seizure of power are entering their sixth week.
In Yangon, a video posted on social media showed crowds of people, some wearing hard hats and gas masks, running down a street as the sound of gunfire is heard.
The demonstrators quickly sprayed vapour from fire extinguishers as they retreated.
The use of fire extinguishers – common now in protests across Myanmar – is intended to smother tear gas and also create a screen that makes it harder for police to pursue or shoot at demonstrators.
There were also reports of injuries from live rounds and rubber bullets in other parts of Yangon, including Insein Township, where black smoke could be seen after security forces reportedly set roadblocks on fire.
State-run media announced late Sunday that Yangon's massive Hlaing Tharyar township and the neighbouring Shwepyitha township will be placed under martial law.
The vast and impoverished townships are known as factory hubs and home to garment factories.
The junta "gives administrative and judicial martial law power to the Yangon regional commander... to perform security, maintain the rule of law and tranquility more effectively," said an announcer on state-run TV.
On Saturday, the civilian leader of Myanmar’s government in hiding vowed to continue supporting a “revolution” to oust the military leaders who seized power in the February 1 coup.
Mahn Win Khaing Than, who was named the acting vice president by Myanmar's ousted politicians and is a member of deposed leader Aung San Suu Kyi's political party, addressed the public for the first time since the coup.
"This is the darkest moment of the nation and the moment that the dawn is close.
“In order to form a federal democracy, which all ethnic brothers who have been suffering various kinds of oppressions from the dictatorship for decades really desired, this revolution is the chance for us to put our efforts together,” he said.
Mahn Win Khaing Than, who is on the run along with most senior officials from the ruling National League for Democracy Party, said the civilian government would seek to give people the legal right to defend themselves.
At the end of the message, he flashed the three-finger salute that has become a symbol of resistance to the military rulers.
More than 80 people had been killed and 2,100 arrested as of Saturday in widespread protests against the military coup, the Assistance Association for Political Prisoners advocacy group said.
At least 13 people were killed on Saturday, one of the bloodiest days since the coup, witnesses and domestic media said, as hundreds of people demonstrated in different parts of Yangon after putting up barricades of barbed wire and sandbags to block security forces.
In one area, people staged a sit-in protest under sheets of tarpaulin rigged up to protect them from the harsh midday sun. "We need justice," they chanted.
"They are acting like they are in a war zone, with unarmed people," said Myat Thu, an activist in the city of Mandalay.
Junta-run media MRTV's evening news broadcast on Saturday called the protesters criminals but did not elaborate.
