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Hundreds of people gathered at the Donka hospital in predominantly Muslim Guinea's capital to visit the injured and identify the dead.
A Reuters reporter saw the bodies of three children among the dead, while witnesses put the number at around 10.
"There are currently 34 bodies in the morgue. The list of injured keeps growing," a medical source told Reuters, requesting anonymity. "The oldest among them can't be more than 20. There are young girls among them," he said.
The presidency declared a week of mourning. The head of a government agency for entertainment was removed from his post following the incident overnight, the presidency added.
Witnesses said the event was attended by up to 10,000 people, mostly children and young people, who came to see popular local rap groups 'Banlieuzart' and 'Instinct Killers'.
Adama Bah, a promoter who attended the event in the Ratoma neighbourhood, said it was overcrowded and that he saw only about a dozen police officers on the site.
"When I saw that crowd, with all the people jostling, some children choking, I understood that there would be a tragedy and I told the organisers, who weren't listening to me," said Bah.
The event's promoter Abdoulaye Mbaye did not respond to several attempts to contact him by telephone.
A senior police source said that Mbaye was called into the station on Wednesday alongside two other people involved in the event.
In January, six youths were killed on another beach in Conakry when a bridge collapsed during New Year's celebrations. Conakry's beaches are small compared to other regional capitals like Dakar and Freetown and entrances and exits are often narrow.
The stampede came at a time when health workers are stretched by an outbreak of Ebola. The deadly tropical virus was first detected in the poor, mineral-rich West African country in February and has since spread to Liberia and Sierra Leone, killing more than 670 people, according to the World Health Organization.