HAVANA (REUTERS) - Tropical Storm Elsa strengthened late on Sunday (July 4) as its center approached south-central Cuba with the Caribbean island nation's government issuing hurricane warnings for the provinces of Cienfuegos and Matanzas.

The US National Hurricane Center (NHC) forecast Elsa would strengthen some more before it moves over Cuba.

Elsa had arrived earlier in the day in eastern Cuba, whipping palms with strong winds and bringing a steady downpour along parts of the southern coast.

Miami-based NHC said data from an aircraft indicated maximum sustained winds were near 65 miles per hour (100 km per hour) with higher gusts.

It had downgraded Elsa from a hurricane on Saturday. A hurricane is defined as having winds of at least 75 mph (121 kph).

"There is a lot of wind and waves of a metre or more," Wilfredo Munoz Lopez, who rents rooms to tourists on Cabo Cruz, said by phone.

"There is no one out. Everyone is in their home or shelters, as we expect it to get worse."

Local forecasters are warning of intense rain for days with the worst in central and perhaps western Cuba.

"There is not much wind but a lot of rain, even for this area," said homemaker Misladi Pulgar in the foothills of the Sierra Maestra Mountains, inland from Cabo Cruz.

"They evacuated everyone living near the rivers and reservoirs."

According to provincial reports, more than 100,000 people have been evacuated in the potential path of the storm, most to homes of family and friends, but thousands also to government shelters.

Evacuations were underway as far west as the capital Havana for fear that rains over the next few days could cause the collapse of dilapidated buildings.

This has raised concerns as the country is experiencing a surge of the coronavirus with a transmission rate of more than 10 per cent on Saturday, twice what often triggers a lockdown.

Elsa's centre was 265km east-south-east of Cayo Largo and about 440km south-east of Havana at 11pm ET (11am Monday Singapore time), the NHC said, and heading northwest at 24 kph.

The storm will bring 13 to 25cm of rain to Cuba, with some spots getting up to 38cm. The NHC said this would result in significant flash flooding and mud slides.

Cuba's southern coast is forecast to receive a storm surge of up to 1.5m

Elsa is forecast to continue to approach central Cuba late on Sunday and early Monday, before heading toward the Florida Strait on Monday and pass near the Florida Keys early Tuesday.

Tornadoes are possible across southern Florida on Monday afternoon and into Tuesday, the Miami-based NHC said in an alert.

The approaching storm has forced Florida officials to demolish the remaining portion of a condo building that collapsed 11 days ago, killing at least 24 with over 120 people missing.

Others in the region were still grappling with the fallout on Sunday. Authorities in Haiti, where the storm has severely affected the agriculture sector, according to an initial assessment, warned of a risk of floods and landslides.

In Jamaica's capital Kingston, some roads were flooded. "Persons have been trapped in vehicles," Owen Palmer, a first responder said, adding that some residents were scared. "They didn't take the storm seriously - as Jamaicans always do - until the rain started to fall."

Iane Thomas, who runs a small restaurant, said a swollen river flooded nearby houses. "The river was running very fast cause plenty rain fell in the morning. It came down from the hills," Thomas said.