After leaving more than 50 people dead in Haiti, Tropical Storm Fay was expected to reach Florida late Monday and take a path across the southern US state.

The storm was forecast to strengthen into a hurricane as it neared the south-western Florida coast, which the National Hurricane Centre in Miami had placed under a hurricane warning.

Fay earlier crossed over Cuba and hurricane warnings there had been discontinued. US forecasters said 10 to 20 centimetres of rain could fall in Cuba, prompting flash floods and mud slides. There had been no reports of the extent of the damages on the communist island.

In Haiti, a lorry carrying more than 70 passengers was swept off a road into a river, and only 25 people were believed to have survived the accident, local media reported. Seven other people had died in flooding and landslides.

Four people were killed by the storm in the neighbouring Dominican Republic.

The storm moving north-north-west at 20 kilometres per hour was to reach the Florida Keys by Monday afternoon or evening, bringing high storm tides, strong winds and heavy rain, forecasters said.

Its winds were reaching speeds of 95 kilometres per hour, and could already be felt in some parts of the Keys and south-eastern Florida on Monday morning.

Fay could also dump 10 to 20 centimetres of rain in Florida and 7 to 13 centimetres of rain in the Bahamas.