(Updates with detail, comment from protests)
* Protesters back out after two killed in Mandalay
* Towns across the country see peaceful protests
* U.S. 'deeply concerned' by violence
* Facebook removes main military page for inciting violence
Feb 21 (Reuters) - Huge crowds marched in Myanmar on Sunday to denounce a Feb. 1 military coup in a show of defiance after the bloodiest episode of the campaign for democracy the previous day, when security forces fired on protesters, killing two.
The military has been unable to quell the demonstrations and a civil disobedience campaign of strikes against the coup and the detention of elected leader Aung San Suu Kyi and others, even with a promise of new elections and stern warnings against dissent.
Tens of thousands of people massed peacefully in the second city of Mandalay, where Saturday's killings took place, witnesses said.
"They aimed at the heads of unarmed civilians. They aimed at our future," a young protester told the crowd.
Military spokesman Zaw Min Tun has not responded to attempts by Reuters to contact him by telephone for comment.
He told a news conference on Tuesday the army's actions were within the constitution and supported by most people, and he blamed protesters for instigating violence.
In the main city of Yangon, thousands of mostly young people gathered at different sites to chant slogans and sing.
"Us young people have our dreams but this military coup has created so many obstacles," said Ko Pay in Yangon. "That's why we come out to the front of the protests."
In Myitkyina in the north, people laid flowers for the dead protesters. Big crowds marched in the central towns of Monywa and Bagan, in Dawei and Myeik in the south, Myawaddy in the east and Lashio in the northeast, posted pictures showed.
At the tourist spot of Inle Lake, people including Buddhist monks took to a flotilla of boats holding aloft portraits of Suu Kyi and signs saying "military coup - end".
The more than two weeks of protests had been largely peaceful until Saturday, unlike previous episodes of opposition during nearly half a century of direct military rule to 2011.
The violence looked unlikely to end the agitation.
"The number of people will increase ... We won't stop," protester Yin Nyein Hmway said in Yangon.
The trouble in Mandalay began with confrontations between the security forces and striking shipyard workers.
Video clips on social media showed members of the security forces firing at protesters and witnesses said they found the spent cartridges of live rounds.
U.N. Special Rapporteur for Myanmar Tom Andrews said he was horrified by the deaths of the two, one of them a teenaged boy.
"From water cannons to rubber bullets to tear gas and now hardened troops firing point blank at peaceful protesters. This madness must end, now," he said on Twitter.
The state-run Global New Light of Myanmar newspaper said the strikers sabotaged boats at the city's river port and attacked police with sticks, knives and catapults. Eight policemen and several soldiers were injured, it said.
"Some of the aggressive protesters were also injured due to the security measures conducted by the security force in accordance with the law," the newspaper said without mentioning the deaths.
Suu Kyi's National League for Democracy (NLD) condemned the violence by security forces in Mandalay as a crime against humanity.
A young woman protester, Mya Thwate Thwate Khaing, became the first death among the demonstrators on Friday. She was shot in the head on Feb. 9 in the capital Naypyitaw.
Hundreds of people attended her funeral on Sunday.
Military media said the bullet that killed her did not come from any gun used by police and so must have been fired by an "external weapon".
The army says one policeman has died of injuries sustained in a protest.
The army seized power after alleging fraud in Nov. 8 elections that the NLD swept, detaining Suu Kyi and others. The electoral commission dismissed the fraud complaints.
Facebook deleted the military's main page for repeated violations of its standards "prohibiting incitement of violence and coordinating harm" and Western countries that condemned the coup decried the violence.
U.S. State Department spokesman Ned Price said the United States was "deeply concerned".
France, Singapore, Britain and Germany also condemned the violence while U.N. Secretary-General Antonio Guterres said lethal force was unacceptable.
The United States, Britain and others have announced limited sanctions, focusing on military leaders, but the generals have long shrugged off foreign 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.
A rights group said 569 people have been detained in connection with the coup. (Reporting by Reuters staff Writing by Robert Birsel Editing by William Mallard, Lincoln Feast and Frances Kerry)