US Secretary of State Marco Rubio said Washington was seeking its own facts about the shooting and would "respond accordingly."

"We're not going to base our conclusions on what they've (Cuba) told us, and I'm very, very confident that we will know the full story of what happened here," Rubio told reporters while on a trip to the Caribbean nation of St Kitts and Nevis.

"As we gather more information, then we'll be prepared to respond accordingly," he said.

The attorney general of Florida, which lies just 100 miles (160 kilometers) from Cuba across the Florida Straits, ordered an investigation into the killings.

The Cuban interior ministry earlier said the coast guard encountered the "illegal" US vessel, whose registration number it gave as FL7726SH, one nautical mile from Cayo Falcones island off Cuba's northern coast.

As the coast guard vessel approached, "shots were fired from the illegal speedboat," injuring the commander of the Cuban vessel, the ministry said.