An AP reporter spotted the family earlier Tuesday beside their boat at the marina. A man who resembled photographs of Joshua Michael Hakken yelled out "Stop! Stay back!" as the reporter approached, but there was no outward sign of tension or distress between the family members.
Tablada said the Foreign Ministry had informed U.S. diplomats on the island "of the Cuban government's willingness to turn over ... U.S. citizens Joshua Michael Hakken, his wife Sharyn Patricia and their two minor sons."
She said Cuba tipped the State Department off to the Hakkens' presence on Sunday and that from that moment "diplomatic contact has been exchanged and a professional and constant communication has been maintained."
U.S. authorities say Hakken kidnapped his sons, 4-year-old Cole and 2-year-old Chase, from his mother-in-law's house north of Tampa. The boys' maternal grandparents had been granted permanent custody of the boys last week.
The U.S. and Cuba share no extradition agreement and the island nation is also not a signatory of the Hague Convention on the Civil Aspects of International Child Abduction, an international treaty for governmental cooperation on such cases.
Cuba has harbored U.S. fugitives in the past, though most of those cases date back to the 1960s and 70s, when the island became a refuge for members of the Black Panthers and other militant groups. More recently, dozens of Cuban Medicare fraud fugitives in the U.S. have tried to escape prosecution by returning to the island.
But Cuba has also cooperated with U.S. authorities in returning several criminal fugitives in recent years.
Hakken lost custody of his sons last year after a drug possession arrest in Louisiana and later tried to take the children from a foster home at gunpoint, authorities said. A warrant has been issued for his arrest on two counts of kidnapping; interference with child custody; child neglect; false imprisonment and other charges.
According to the Hillsborough County Sheriff's Office, Hakken entered his mother-in-law's Florida house last Wednesday, tied her up and fled with his sons. Federal, state and local authorities searched by air and sea for a boat Hakken had recently bought. The truck Hakken, his wife and the boys had been traveling in was found Thursday, abandoned in Madeira Beach, Florida.
"He'll have to face in Hillsborough county the charges he has with the sheriff's office," spokeswoman Cristal Bermudez Nunez Nunez said. She said she did not know how the family would be returned or what will happen when they arrive on U.S. soil.
Terri Durdaller, a spokeswoman at the Florida Department of Children and Families, said it was not clear where the children will ultimately be placed.
"Louisiana is the ultimate decision maker on where these children will reside. It's likely they will be placed back in Florida with the grandmother," she said.
The Hakkens' flight to Cuba recalls the child custody case that set Cold War foes Washington and Havana feuding in 1999. That year, 5-year-old Elian Gonzalez was found clinging to an inner tube off Florida after his mother and others drowned while fleeing Cuba toward American soil. The boy was taken to Miami to live with relatives, but his father in Cuba demanded the boy be sent back.
U.S. courts ultimately ruled Gonzalez should be sent back, though his Miami relatives refused to return him. In April 2000, U.S. federal agents raided the family's home and he was returned to Cuba soon after. He has since grown into a young man and joined a military academy.
At the Havana marina on Tuesday, the family showed no sign they knew a decision about their fate had been made. The four strolled by an outdoor restaurant as security officials kept reporters at a distance.
The youngest child was seated in a stroller and the elder boy sat down on a curb. A woman who resembled Sharyn Hakken was seen on the boat.
Cuban officials told reporters not to take pictures of the family or the boat, which bore the name Salty and had a paw print on its side.
Andrew Zych, a Canadian docked in a sailboat steps away from the Hakkens, said the family had arrived recently and seemed normal.
"I liked the way they played with the kids," he said, adding he was surprised to learn of events in the United States.