By Stephen Gibbs
BBC News, Havana
The governments of Cuba and the US have both blamed each other for the apparent deaths of 31 Cubans believed drowned while trying to leave Cuba on a boat.
Just three people survived after the speedboat reportedly overturned on 16 August, between Cuba and Florida.
The US Coast Guard, who say they are dealing with a surge in Cubans crossing the Florida Straits, called off its search for survivors on Wednesday.
But mystery still surrounds the precise circumstances of the shipwreck.
Two women and a man were found drifting at sea by a merchant ship around 50km north of the Cuban coast last week.
They had apparently been in the water for five days after their boat capsized.
They were brought back to Cuba, suffering from severe sunburn and dehydration.
The 31 passengers believed to be on the same speedboat are all now assumed drowned.
Cuba says that the US is responsible. Appearing on state television, President Fidel Castro blamed US immigration policy whereby Cubans who make it to American soil are usually granted automatic asylum.
He described it as an incentive for Cubans to risk their lives in the dangerous voyage.
Cuba is also calling on the American authorities to do more to stop professional people smugglers who charge around $8,000 (£4,440) a head for a fast boat crossing from Cuba to Florida.
But the United States has retorted, saying Cuba is cynically trying to deflect blame from itself for the tragedy.
A strongly-worded statement released by the US Interests Section in Havana says those who died were attempting to flee political repression and government-inflicted impoverishment.
It says that while the US Coast Guard searched for survivors, Cuba did not.
It accuses the Cuban authorities of showing a blatant disregard for their citizens' welfare.