Protesters gathered all over Myanmar again on Sunday, a day after security forces shot dead two people at a demonstration in the country's second biggest city.

A funeral was also held for a young woman killed earlier by police.

Mya Thwet Thwet Khine was the first confirmed death among the many thousands who have taken to the streets in protest at the February 1 coup that toppled the elected government of Aung San Suu Kyi.

She was shot on February 9, two days before her 20th birthday, during a protest in the capital, Nayptitaw, and died on Friday.

About 1,000 people in cars and bikes gathered on Sunday morning at the hospital where her body was being held amid tight security, with even the victim's grandparents who had travelled from Yangon, five hours away, denied entry.

When her body was released, a long procession of vehicles drove to the cemetery.

In Yangon, Myanmar's biggest city, about 1,000 demonstrators honoured her under a flyover.

"I want to say through the media to the dictator and his associates, we are peaceful demonstrators," said protester Min Htet Naing. "Stop the genocide! Stop using lethal weapons!"

Another large protest took place in Mandalay, where police shot dead two people on Saturday near a dockyard as security forces were trying to force workers to load a boat.

The workers, like railway workers and truckers and many civil servants, have been taking part in a civil disobedience campaign against the junta.

Shooting broke out after neighbourhood residents rushed to the Yadanabon dock to try to assist the workers in their resistance.

One of the victims, described as a teenage boy, was shot in the head and died immediately, while another was shot in the chest and died on the way to hospital.

Several other serious injuries were also reported.

Witness accounts and photos of bullet casings indicated that the security forces used live ammunition, in addition to rubber bullets, water cannons and slingshots.

The new deaths drew a quick and strong reaction from the international community.

"The shooting of peaceful protesters in is beyond the pale," said UK Foreign Secretary Dominic Raab on Twitter. "We will consider further action, with our international partners, against those crushing democracy & choking dissent."

Britain last week froze assets of and imposed travel bans on three top Myanmar generals, adding to already existing targeted sanctions.

Singapore, which together with Myanmar is part of the 10-member Association of Southeast Asian Nations, issued a statement condemning the use of lethal force as "inexcusable".

Urging "utmost restraint" on the part of security forces, it warned that "if the situation continues to escalate, there will be serious adverse consequences for Myanmar and the region".

Another fatal shooting took place on Saturday night in Yangon in unclear circumstances.

According to several accounts on social media, including a live broadcast that showed the body, the victim was a man who was acting as a volunteer guard for a neighbourhood watch group.

Such groups were established because of fears that authorities were using criminals released from prison to spread panic and fear by setting fires and committing violent acts.

Another live broadcast on Facebook showed the wife of actor Lu Min describing to neighbours how her husband was arrested and taken away from their home shortly after midnight.

He was one of six high-profile people in the entertainment industry charged last week with inciting civil servants to stop work and join the protest movement, which he and the others have publicly championed.

On Sunday, Facebook announced that it had taken down the page run by the Myanmar military information unit "for repeated violations of our community standards prohibiting incitement of violence and coordinating harm". It had already removed other accounts linked to the military.

The junta took power after detaining Ms Suu Kyi and preventing Parliament from convening, saying elections last November were tainted by voting irregularities.

The election outcome, in which Ms Suu Kyi's National League for Democracy party won by a landslide, was affirmed by an election commission that has since been replaced by the military. The junta said it will hold new elections in a year's time.

The coup was a major setback to Myanmar's transition to democracy after 50 years of army rule which began with a coup in 1962.

Ms Suu Kyi came to power after her party won a 2015 election, but the generals retained substantial power under the constitution, which was adopted under a military regime.