The block of flats caved in on Tuesday evening and rescuers have so far pulled more than 50 people from the wreckage.
Heavy lifting equipment arrived at the site to help people using their bare hands to reach those inside.
Lagos state governor Bola Tinubu vowed to prosecute those responsible for allegedly shoddy construction of the 36-flat complex, news agency AP said.
More than 100 people are feared to have been in the building when it collapsed, according to the AFP news agency.
A BBC correspondent at the scene says there are fears for those still trapped in the rubble as they are no longer reachable by mobile phone.
Trapped people
"We are still hopeful that more people will be brought out alive as rescue work progresses," said Red Cross worker Umar Mairiga told Reuters news agency.
Overnight, distraught relative were in touch with those inside, but the calls had stopped by morning. Rescuers had said they had heard trapped people crying out for help.
Crowds cheered as a woman was brought out alive on Wednesday morning, AP reported.
But police later had to beat off crowds of upset relatives looking for missing relatives on Wednesday.
"I was coming out of my house when I heard a loud bang and the four-storey structure suddenly caved in"
The collapse happened after many of the occupants had returned from work on Tuesday evening.
"It was a gory sight. I was coming out of my house when I heard a loud bang and the four-storey structure suddenly caved in," eyewitness Debo Ajala told AFP.
Lagos state police spokesman, Bode Ojajuni, said the authorities had launched an investigation into the cause of the collapse, the agency reports. The building is thought to have housed some 180 people in the 36 apartments.
Our correspondent says the building in the residential area of Ebute Metta was relatively new - thought to be not more than three years old.
Such collapses in the past have been blamed on substandard construction and flouting of building regulations, he says.
Dozens have died in recent years in Lagos as poorly maintained buildings have collapsed.
In March, one of Lagos' tallest buildings caved in during a heavy thunderstorm in the heart of the commercial district. The building had been sealed off after a fire on the eighth floor.
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