Monday’s massive turnout, accompanied by the closure of many shops and other places of work, comes after police fired on protesters on Saturday, killing two people. More than 30 others were injured in the incident, which took place in the city of Mandalay. A message on state-run TV late Sunday warned that protesters were pushing people down a path of confrontation where they would suffer a loss of life.

The demonstrations don’t have a leader, but participants have mobilized crowds using phone calls, texts, live-streaming, messaging apps like Signal and social-media websites to exchange plans and alert fellow protesters.

Arising at 5 a.m. Monday, Thaw Zin drove around Myanmar’s largest city, Yangon, to map out the locations of police barricades, street closures and convoys of military vehicles—details he shared with a core group of friends, whom he calls “proliferators of information,” who in turn relayed the tidbits to others to help plan the day’s demonstrations. An hour later, he was at a prominent protest site, hanging up posters from an overpass before police arrived.

Each day for two weeks, Mr. Thaw Zin, who runs an internet startup, has showed up to oppose the coup, which he says was “a total violation of the people’s mandate.” His Fitbit, the wearable fitness device, shows he’s clocked 185 miles in that time, marching through the streets and traveling from one protest site to another by foot to avoid traffic snarls, he said. He is also part of his neighborhood’s watch group—volunteers who keep nightly vigil, alert residents to the arrival of police trucks and guard against people he says are sowing chaos. He carries a long wooden stick, a hammer and a knife on nighttime patrols.

Mr. Thaw Zin knows all about the military’s past crackdowns. He was 14 years old when security forces shot protesters to end a 2007 pro-democracy uprising. But this time, he says, is different. The military has pledged to hold elections and, although Mr. Thaw Zin and others believe any such vote would ultimately be designed to favor the army-backed party and severely disadvantage the pro-democracy side, the generals are nevertheless seeking legitimacy, he said. That is why, he hopes, they might exercise greater restraint.

“This struggle is extremely important,” he said. “The country has a strong culture of military intervention in politics. Now people are saying, ‘We can’t have this anymore.’”

Some protesters described Monday’s demonstrations as the “22222 strike” after the date, Feb. 22, 2021. They carried posters bearing the images of those who had died, including a young woman struck in the head by a bullet in the country’s capital in the early days of protests. Many, including government employees, boycotted work, broadening a civil-disobedience movement that has steadily gained steam.

Events in Myanmar are being closely followed in Washington. In a tweet Sunday, State Department spokesman Ned Price said, “We continue to stand with the people of Burma as they voice their aspirations for peace, democracy, and rule of law,” referring to the country by its former name, which the U.S. government still employs.

Myanmar’s foreign ministry has called the demonstrations unlawful and said authorities are exercising restraint. In a weekend post on its official Facebook page, it said some statements made by foreign countries “are tantamount to flagrant interference in internal affairs of Myanmar.”

Write to Niharika Mandhana at niharika.mandhana@wsj.com