Rescuers say many may have still be buried under the rubble of the building.
An initial report had said that at least 20 people were killed in the disaster while 50 others were injured.
Witnesses said the building collapsed with a "bang" just as residents were coming home from work on Tuesday night.
An AFP reporter who visited the scene early on Wednesday heard wails and cries from people trapped in the debris. "Please help me, I am dying," one victim cried out.
A man who simply gave his name as David said that his wife and three children were still under the building.
Red Cross disaster officer Umar Mairiga rescuers were battling to save more people.
Mr Mairiga said more than 100 people were believed to have been "either inside or around the vicinity" of the building when it collapsed. It contained 36 flats, a penthouse and some shops.
"There is no doubt that people are still buried under the belly of the earth. That is why we have to step up efforts to save them," he said.
Witnesses said a group of people were seen drinking at a liqour shop in front of the building when it collapsed.
Neighbours quickly moved in to rescue people using their hands to pull them from the rubble but dozens were still believed to be trapped.
Heavy lifting equipment arrived at the site to help people using their bare hands to reach those inside.
Lagos State Governor Bola Tinubu who visited the scene of the disaster ordered the immediate arrest and prosecution of those responsible for the construction of the building.
He also appealed to onlookers and relatives to leave the scene to allow for a smooth rescue operation.
Authorities have launched an investigation into the cause of the tragedy, the latest in a string of such disasters in Africa's most populous country in recent months, especially in overcrowded Lagos.
Building experts have blamed the collapses on the use of substandard construction materials, disregard for building regulations and non-compliance with development policies.
A structural engineer, Bayo Adeola, said that the collapse must have been due to lack of professional handling of the building project or the use of poor materials.
The Nigerian Institute of Building (NIOB) said 84 buildings had collapsed in Nigeria for the past 20 years, claiming more than 400 lives.
The institute said the figure could be more since it based its claim on reported cases.
In March an 18-storey building belonging to the state-run Bank of Industry suddenly collapsed, injuring several people.
Last year the owner of a three-storey building that collapsed, killing four people and injuring many others, was arrested for altering the original one-storey structure without approval.