Security forces were also deployed at hospitals and universities, state media said.
Two of the victims died of gunshot wounds to the head in the northern town of Myitkyina, the witnesses said. It was not immediately clear who fired on the protesters although both police and the military were at the scene, Reuters wrote.
Photos posted on Facebook showed the bodies of two men lying on the street. Witnesses said they were taking part in a protest against the coup when police fired stun grenades and tear gas. Several people were then hit by gunfire from nearby buildings.
One witness, who said he helped move the bodies, said two people were shot in the head and died on the spot. Three people were wounded.
“How inhumane to kill unarmed civilians,” said the witness, a 20-year-old man. “We must have our right to protest peacefully.”
Police and military have killed more than 50 people to quell the daily demonstrations and strikes against the Feb. 1 coup, according to the United Nations.
Myanmar has been in turmoil since the Army overthrew the elected government of Aug Sang Suu Kyi, detained her and other political figures, and installed a military government.
The generals say they acted because an election in November which saw Suu Kyi’s National League for Democracy (NLS) secure a big victory was marred by fraud – a claim rejected by the electoral commission.
They have promised to hold another election, without giving a date. In the meantime, security forces have cracked down hard on widespread pro-democracy protests, with last week the bloodiest so far in a country that has a history of military rule and crushing of dissent.
On Monday, demonstrators gathered in Yangon and in the second-biggest city Mandalay and several other towns, according to videos.
Protesters in Dawei, a coastal town in the south, were protected by the Karen National Union, an ethnic armed group engaged a long-running war with the military.
Witnesses reported sounds of gunfire or stun grenades in many districts of Yangon after nightfall as soldiers set up camp in hospitals and university compounds. It was not clear whether anyone was hurt.
The international Physicians for Human Rights (PHR) organization protested against the occupation of the hospitals, which it said was a violation of international law.
At least nine unions covering sectors including construction, agriculture and manufacturing have called on “all Myanmar people” to stop work to reverse the coup and restore Suu Kyi’s government.
Allowing business and economic activity to continue would help the military “as they repress the energy of the Myanmar people”, the unions said in a statement.
“The time to take action in defense of our democracy is now.”
An NLD official and local campaign manager, Khin Maung Latt died in police custody on Sunday. Ba Myo Thein, a deposed lawmaker, said reports of bruising to Khin Maung Latt’s head and body raised suspicions that he had been “tortured severely”.
Figures by the Assistance Association for Political Prisoners advocacy group showed nearly 1,800 people have been detained under the junta as of Sunday.
An announcement by the military carried on the front page of the State-run Global New Light of Myanmar newspaper on Monday threatened unspecified action against anyone who directly or indirectly works for a committee of ousted lawmakers that has declared itself the country’s legitimate authority.
The announcement said the committee was illegal and had committed “high treason”.