Rescue workers rushed to dig survivors from the rubble in downtown Nairobi but have been hampered by thousands of onlookers.
The building was under construction when it collapsed, trapping workers beneath the wreckage.
The head of disaster operations with the Kenya Red Cross Society, Farid AbdulKadir, told AFP seven bodies were removed from the debris.
"As of now, seven people died at the scene of the accident," he said.
Another three died later in Kenyatta National Hospital, where at least 75 people were admitted.
"We have managed to pull out 17 people alive from the debris but as each second passes, the chances of saving those under the rubble diminishes," Mr AbdulKadir said.
Volunteer rescuer Calvince Omondi said trapped survivors had made contact with rescuers.
"Several people are still trapped in the basement and we can communicate with them," he said to AFP.
"They say they are lacking oxygen."
Simon Githai, a spokesman at the Kenyatta hospital, told AFP at least 18 of those admitted were in serious condition.
Most others were being treated for minor wounds and broken bones.
As darkness fell, two people were injured when a bus driver lost control of his vehicle near the scene and it ploughed into a triage area.
Crowds hinder rescue
By late afternoon, rescue teams backed with bulldozers fought large numbers of curious bystanders to get to the site.
Rescuers used heavy equipment to dig through the debris, cut steel rods with power saws and smashed concrete with sledge hammers.
Witnesses say authorities were initially unsure how to block off the area from the crowds.
Anti-riot police and troops later arrived on the scene to restore order.
Kenya’s President Mwai Kibaki has cut short a trip to Sudan for a summit of African Union leaders, to co-ordinate relief efforts and comfort the victims’ families.
"It was regrettable that innocent lives have been lost in the tragedy, which would have easily been prevented," a statement issued by his office said.
"All the necessary government machinery had been mobilised to minimise further loss of lives and injuries," it said.
Investigation begins
Police Inspector Matthew Limo said initial investigations suggested the ollapse was "caused by poor building standards."
Kenyan Housing Minister Soita Shitanda visited the site and agreed with the assessment.
"Looking at the building, it seems something was not done right," Mr Shitanda told reporters.
He suggested the owners ignored or flouted accepted construction standards.
One of the workers rescued from the wreckage, William Njaramba, said construction on the building was rushed.
"I think the problem that caused this collapse is the speed at which we were doing our work," Mr Njaramba said.
“The cement-to-sand ratio was not right (and) they did not give the building time to dry," he said.
Witnesses spoke of seeing a large crack in the building before it collapsed.
"I had finished my lunch and was resting on the fourth floor when suddenly I felt the building caving in under me," said Fredrick Njabari, who arms were broken in the collapse.