In video seen by CNN, a large crowd of people can be seen running away from police and taking cover.
In another video, a person can be seen being stretchered away by medics. The condition of the patient was not immediately clear.
Two different volunteer emergency workers confirmed the latest deaths to agencies.
“Twenty people were injured and two are dead,” said Ko Aung, a leader of the Parahita Darhi volunteer emergency service, told Reuters.
“Two people were killed and about 30 others injured,” AFP reported, citing Hlaing Min Oo, the head of a Mandalay-based volunteer emergency rescue team.
“Half of the injured were shot with live rounds,” he told AFP.
Protests and civil disobedience movements against the military coup on February 1 have been the biggest in decades, with thousands calling for Suu Kyi to be released from detention and power handed back to civilian control.
The Assistance Association for Political Prisoners, a human rights group, said in a statement that it had verified 569 arrests related to the coup since February 1.
However Saturday’s violence does not appear to have deterred protesters from taking to the streets for a 16th consecutive day. On Sunday, demonstrators could be seen on live streams from news agencies chanting slogans and waving flags from motorbikes in Myitkyina, the capital of Kachin state in northern Myanmar.
Facebook said it deleted a page run by the Myanmar military from the social media platform on Sunday for “repeated violations of our Community Standards prohibiting incitement of violence and coordinating harm,” according to a statement provided to Reuters by Rafael Frankel, Facebook’s director of public policy.
CNN has asked Facebook for further details but has not received a response.
Concerns had been growing over the potential for violence in Myanmar as protesters urge supporters to take to the streets in defiance of the military generals who have deployed troops in major cities.
CNN’s Eric Cheung, Sandi Sidhu and Helen Regan contributed this report.