Workers have slogged throughout the day to clear the tons of twisted metal, concrete, glass, and snow. Mayor Yury Luzhkov said it would take several days to clear the entire site.
So far, 58 people have been confirmed dead, and 20 people are still being treated in hospital.
The authorities say it is impossible to put a figure on the number of people who were in the building when the roof caved in at 5:15 a.m., but some survivors said there could have been as many as 200.
'At Least 100 Still Under The Rubble'
An anxious crowd stood at the police cordon surrounding the collapsed building for the second day today, waiting for news of missing relatives and friends.
Gassan, a middle-aged man from Azerbaijan, said that two of his friends who worked at the market had already been confirmed dead, and that several other friends were still missing.
According to him, more than 100 people could still be trapped under the debris, since many vendors lived inside the market. "Azerbaijanis did not live there, Tajiks and Uzbeks lived there. At least 100 people are still under the rubble. They say our friends are not among the dead or the injured. It means they are still there."
A representative from the Emergency Situations Ministry has said that most of the victims were Azerbaijani men who worked at the market.
The vast majority of victims hail from other former Soviet countries, namely Tajikistan, Uzbekistan, Armenia, Georgia, and Ukraine.
The collapse occurred at dawn on 23 February, when the market was still closed to the public. Some vendors, however, were already setting out their stalls while others were working in some parts of the market that are used overnight for wholesale trading.
Many vendors also appear to have lived inside the market, particularly in its basement, and could have been asleep when the roof caved in.
Gulbakhor Sharipova, an elderly Tajik woman, told RFE/RL's Uzbek Service that she lived in the market and that her son, who was inside when the roof collapsed, was still missing.
"We slept there. It was a good market. We don't have a flat. Many came here early in the morning; there were many loaders," Sharipova said. "They let us sleep in the hall, they didn't take money from us for this, I'm not lying. They still haven't retrieved all the people from the basement, an Emergency [Situations] Ministry worker told me this. He said there were many people in the basement. Tajiks and Uzbeks sorted out greens and vegetables there."
A Russian man who ran a trading pavilion on the market's second floor and who wished to remain anonymous confirmed that the market was home to dozens of migrant vendors.
He told RFE/RL that he suspected the authorities of concealing the true death toll: "Many people lived in this market. They had no registration, so nobody knows how many there were. They came for short periods, they worked, they sold, and then quietly left. They lived there. When [the roof] collapsed, they reportedly called from the basement with their mobile phones [and said]: 'help us, we are being flooded.' They want to pull down this building during the night and remove, remove, remove everything. Because it's awful there, you see, they don't let anyone near."
The authorities have dismissed the idea that the vendors also lived in the market. Mayor Luzhkov said today that rescuers had inspected the basement and found no one there.
The Baumansky market victims belong to the millions of migrant workers who come to Russia from impoverished former Soviet republics, where the average wage often amounts to just a few dozen dollars a month.
Most of them have no legal status since employers in Russia are usually reluctant to undergo the complex procedure required to hire foreigners legally. In addition, markets in Russia are often run by criminal groups.
President Vladimir Putin has called for a "painstaking investigation" to establish why the roof of the building, built in the 1970s, collapsed.
Moscow city officials have blamed the weight of snow on the roof. But investigators are also studying whether improper maintenance of the building and construction mistakes could have contributed to the collapse.
Prosecutors have opened a criminal investigation on charges of negligence leading to deaths.
The anonymous Russian entrepreneur said the building was poorly maintained, and has accused the market director of consistently violating security standards: "The director did not carry out any preventive measures or maintenance of the market. Nothing was painted, nothing was inspected. Neither the cables nor the foundations were checked. The market's technical condition was totally neglected."
Moscow Prosecutor Anatoly Zuyev told reporters that the Baumansky market's director has already been called to order in the past. In December 2005, the prosecutor's office reportedly ordered him to bring the market's fire safety system into line with regulations.
(Gulasal Kamalova from RFE/RL's Uzbek Service contributed to this report)