But tension escalated quickly in Mandalay where police and soldiers were confronting striking shipyard workers and other protesters.
Some of the demonstrators fired catapults at police as they played cat and mouse through riverside streets. Police responded with tear gas and gunfire, though it was initially not clear if they were using live ammunition or rubber bullets.
"Twenty people were injured and two are dead," said Ko Aung, a leader of the Parahita Darhi volunteer emergency service agency.
One man died from a head wound, media workers including Lin Khaing, an assistant editor with the Voice of Myanmar media outlet in the city, and a volunteer doctor said.
Ko Aung and the doctor said a second man was shot in the chest and died later of his wound.
Police were not available for comment.
The demonstrations and a civil disobedience campaign of strikes and other disruptions show no sign of dying down. Opponents of the coup are sceptical of the army's promise to hold a new election and hand power to the winner.
A young woman protester died on Friday after being shot in the head last week as police dispersed a crowd in the capital, Naypyitaw, the first death among anti-coup demonstrators.
The army says one policeman died of injuries sustained in a protest.
'SADNESS'
On Saturday, young people in the main city of Yangon carried a wreath and laid flowers at a memorial ceremony for the woman, Mya Thwate Thwate Khaing, while a similar ceremony took place in Naypyitaw.
"The sadness from her death is one thing, but we've also got courage to continue for her sake," said student protester Khin Maw Maw Oo in Naypyitaw.
The demonstrators are demanding the restoration of the elected government and the release of Suu Kyi and others. They have also called for the scrapping of a 2008 constitution that has assured the army a major role in politics since nearly 50 years of direct military rule ended in 2011.
The army seized back power after alleging fraud in Nov. 8 elections that Suu Kyi's National League for Democracy swept, detaining her and others. The electoral commission had dismissed the fraud complaints.
Nevertheless, the army says its action is within the constitution and is supported by a majority of the people. The military has blamed protesters for instigating violence.
Earlier on Saturday, several thousand protesters gathered in the northern town of Myitkyina and confronted lines of police before dispersing.
Crowds also marched again peacefully through the ancient capital of Bagan and in Pathein in the Irrawaddy river delta, pictures on social media showed.
The United States, Britain, Canada and New Zealand have announced limited sanctions, with a focus on military leaders.
Many countries have urged authorities to avoid violence.
Junta leader Min Aung Hlaing was already under sanctions from Western countries following the crackdown on the Rohingya. There is a little history of Myanmar's generals, with closer ties to China and to Russia, giving in to Western pressure.
Suu Kyi faces a charge of violating a Natural Disaster Management Law as well as illegally importing six walkie-talkie radios. Her next court appearance is on March 1.
Myanmar's Assistance Association for Political Prisoners said 546 people had been detained, with 46 released, as of Friday.