Despite calls by the prime minister for "cool heads", tensions over the country's deadliest industrial disaster showed little sign of abating and there were fears of more violence and vandalism at textile mills.
Several thousand workers holding red banners and flags chanted "Hang the killers, Hang the Factory Owners!" as they took to the streets of Dhaka at the start of a series of nationwide demonstrations on what is a public holiday.
Kamrul Anam, one of the leaders of the Bangladesh Textile and Garments Workers League, said the workers were angry at "the murder" of their colleagues in the April 24 disaster at Savar on the outskirts of Dhaka.
"We want the severest punishment possible for those responsible for this tragedy," he told AFP.
Activists were expected to take to the streets across Asia, with tens of thousands expected to rally in Indonesia against outsourcing and low wages while major May Day protests are scheduled for crisis-hit Greece and Spain.
In impoverished Bangladesh, unions said demonstrations would be held in all the major cities.
The first May Day protests were in the capital Dhaka, with police putting the number of demonstrators at around 10,000 although that figure was expected to mushroom later in the day.
The Bangladesh government faces foreign pressure to take credible moves to raise safety standards in the garment industry, with last week's collapse at the Rana Plaza factory complex only the latest in a series of deadly disasters.
A total of seven people have so far been arrested and charged with "death by negligence" over the collapse of the eight-storey building which housed five separate garment factories.
Those charged, who include the overall owner of the building as well as engineers who had given the building the all-clear after cracks were reported, have had to wear bullet proof vests at their court appearances.
Tensions have been further heightened by regular clashes between hardline activists and the police who have been using teargas and rubber bullets to disperse crowds of protesters.
Many of the country's 4,500 garment factories have been closed since last Wednesday, a major blow for the Bangladeshi economy which is powered in large part by the 20-billion-dollar industry.
Speaking to parliament on Tuesday night, Prime Minister Sheikh Hasina urged employees to return to work and criticised reported attacks on some factories.
"I would like to tell the workers to keep their head cool, keep mills and factories operative, otherwise you will end up losing your jobs," she said.
"Who will benefit from vandalism in the mills and factories? If the mills and factories are shut down, they will lose job and will have to return home with empty hands and fight for survival."
According to the army, which has been overseeing the operation to find bodies from the site, the number of dead now stands at 393.
Rescuers say they do not expect to find any more survivors and are using cranes to shift the mountain of rubble.
The United Nations revealed on Tuesday that it had offered to fly in specialist rescue teams only hours after the collapse but the government had decided to handle the operation on its own.
The deputy director general of the UN's International Labour Organization, Gilbert Houngbo, was expected in Dhaka on Wednesday to discuss how to improve safety standards with the government.
A fire at a textile factory last November left 111 people dead, and there have been widespread accusations that safety standards are both too lax and rarely enforced.
Campaigners say Western retailers who source their clothing to Bangladesh must also take a share of the blame.
Leading European brands such as Mango, Primark and Benetton have confirmed that their clothing had been recently made at the Rana Plaza.
Senior European Union officials said Brussels was ready to help Bangladeshi authorities meet international standards and urged foreign companies to promote better health and safety standards in garment factories in Bangladesh.
"The European Union calls upon the Bangladeshi authorities to act immediately to ensure that factories across the country comply with international labour standards," EU foreign affairs chief Catherine Ashton and Trade Commissioner Karel De Gucht said in a statement.