Hundreds of rescuers joined the search effort to free people from the wreckage of La Promesse College, a church-run school in the suburb of Petionville.
But the Associated Press reports that crowds of onlookers and desperate relatives of those missing have hampered the arrival of heavy machinery.
Engineers from MINUSTAH, the UN mission in Haiti, and members of the Haitian Red Cross were at the scene, helping remove heavy pieces of concrete, while UN peacekeepers and local police held back the crowds.
Some rescuers have been digging through the rubble with their bare hands.
The site contains a kindergarten as well as a primary and secondary school and it is thought there were between 200 and 700 children inside the building when the first floor caved in.
The US has said it is sending a team of experts, rescue dogs and specialist equipment to Haiti and was working alongside the Haitian government to provide immediate assistance.
"This is a tragic situation, especially since children are involved," said USAID administrator Henrietta Fore.
Neighbouring Dominican Republic has promised to send two helicopters to help the rescue effort.
Nadia Lochard, of the civil protection bureau, said it could confirm 50 teachers and children had died and dozens were injured.
I saw all the kids getting pulled out. But I didn't see mine
Nicholas, Haitian parent
She said "numerous" children were trapped in the rubble.
"We have signs that they are still alive and we are organising help to try to save them," said Ms Lochard.
Rescuers fear many more people are still trapped in the rubble
Relatives gathered around the school, crying and screaming and searching for their children.
"I have four kids in this school and I have not found any of them," said one woman.
One man, Nicholas, said he heard a crash and thought it could be the school.
"When I got there I saw all the kids getting pulled out. But I didn't see mine," he said.
Josiane Dandin said her 15-year-old son had been killed. "He's my only son, I don't know what I'm going to do," she said.
There has been no official comment on the cause of the collapse, but the BBC's Andy Gallacher says residents in the area suspect the school was poorly rebuilt after it partially collapsed several years ago.
Witnesses said one floor collapsed, bringing down the rest of the building
Reports say that the upper floor of the school was still under construction.
A French teacher at the school, Jimmy Germain, said people living downhill from the school had abandoned their land, fearing the building could collapse.
Associated Press quoted police as saying that the preacher who ran the school could face criminal charges.
Haitian President Rene Preval visited the site to comfort relatives and oversee rescue efforts.
He said: "What's important to us now, beside all the sorrow and sadness we feel for the families, is to bring help to those who are still under the rubble and see if we can get them out."
Meanwhile, officials said an investigation would be launched.
"We are going to ask the minister of education to make an inspection of all the schools built in the same way," Senator Yvon Bissereth told AFP.
He appealed for heavy search and rescue equipment to be sent to the island.
Correspondents say Haiti is the poorest nation in the western hemisphere where mudslides and poor construction are commonplace.
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