At least one American citizen was shot dead and another injured by Cuban officials intercepting a speedboat off its coast on Wednesday, a US official has said.

Border guards shot dead four people and injured the remaining six aboard the Florida-registered speedboat. Cuba accused the 10 people on the boat of planning "an infiltration with terrorist aims" and said they opened fire first.

A third person was on a US K-1 visa - for fiancées of American citizens - the US official said. The boat's owner alleged the vessel had been stolen by an employee.

US Secretary of State Marco Rubio had said Washington was investigating the "highly unusual" incident.

Cuban authorities had said all 10 were Cuban nationals residing in the US.