As Ernesto neared Islamorada, south of Miami, the National Hurricane Centre (NHC) lifted all hurricane watches for Florida, but did not rule out the possibility Ernesto might regain its punch later in the week when it could make a second US landfall in South Carolina.
Meanwhile, on the Pacific coast, the more powerful Hurricane John is thought likely to gather pace just off Mexico.
The category three hurricane does not look likely to hit land imminently, but may increase even further in strength, the NHC said.
Ernesto weakens
Contrary to expectations, Ernesto did not strengthen after leaving the Cuban coast, and its maximum sustained winds remained at 72kph as it crossed the Straits of Florida.
The most likely track has the storm travelling along south Florida, heading back out to sea and eventually coming ashore again in South Carolina, according to the NHC.
On Sunday, Ernesto had strengthened into the first Atlantic hurricane of the year, before losing power yesterday as it moved over mountainous areas of Cuba.
Experts initially feared Ernesto would hit Florida as a powerful hurricane packing the same intensity as Katrina, which killed 1,500 people after it slammed ashore near New Orleans, Louisiana, on August 29 last year.
The initial concern prompted Florida Governor Jeb Bush to declare a state of emergency, while visitors were ordered to leave the Florida Keys.
Ernesto's centre was over Plantation Key in the Florida Keys island chain, about 100km south-southwest of Miami, and was moving north-northwest.
Local media in Haiti said the storm killed one person as it blew over the Caribbean island of Hispaniola, which Haiti shares with the Dominican Republic.
There were no immediate reports of casualties in Cuba, where people who fled to safety ahead of the storm started returning to their homes.
Authorities said hundreds of thousands of people had been evacuated before Ernesto hit Cuba.