HAVANA, July 5 (Reuters) - Tropical storm Elsa's center looked set to exit Cuba late on Monday near Havana, churning on track to Florida although the lopsided weather system was expected to dump heavy rains over the Caribbean's largest island in its wake.

At 0900 p.m., the storm's center was 40 km (25 miles) to the south-east of the capital which was still experiencing calm weather conditions, Cuba's Meteorology Institute said, as it crossed the country's center from south to north slowly at 20 km per hour.

Sustained winds were peaking near 85 kmph (50 mph) while storm surges were affecting Cuba's southern coast and would start occurring on the northern coast too, the institute said, causing light flooding in the capital in lower lying coastal areas such as along its famous Malecon seaside corniche.

"The rain is coming behind the centre so the fact it is moving out to sea along the northern coast between Havana and Mayabeque ... does not mean the rain is over," Cuba's best known meteorologist Jose Rubiera said on state television.

More than 100,000 people in Cuba evacuated from flood-prone areas or unsafe housing in the potential path of the storm, most going to homes of family and friends, but thousands also to government shelters, state-run media reported.

While such preparedness has typically enabled Cuba to avoid the kind of casualties from storms seen elsewhere, it comes amid Cuba's worst coronavirus outbreak since the start of the pandemic, raising fears that evacuations could fuel infections.

Elsa already caused at least three direct deaths and some damages to infrastructure and agriculture in Caribbean islands southeast of Cuba like St Lucia and the Dominican Republic.

It comes as the tourism-reliant archipelago is already struggling with the economic fallout from the coronavirus pandemic and bracing for an above-active hurricane season.

Cuban meteorologists said the rains from Elsa could prove positive for agriculture, bolstering water reservoirs, as long as they were not too intense.

Rainfall of 5 to 10 inches (13 to 25 cm) with isolated maximum amounts of 15 inches (38 cm) was forecast across parts of Cuba on Monday night and expected to result in "significant flash flooding and mudslides," the Miami-based U.S. National Hurricane Center (NHC) said.

A tropical storm watch and storm surge watch were in place for much of the western coast of Florida, the NHC said, with Elsa expected to strengthen out at sea as it passed near the Florida Keys early Tuesday and moved near or over portions of the west coast of Florida on Tuesday and Wednesday.

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

But revised predictions showing Elsa tracking to make landfall north of Miami-Dade sparked renewed optimism that the search for survivors would remain uninterrupted.

The NHC said amounts of 3 inches to 5 inches (8 to 13 cm)with localized maximum totals up to 8 inches (20 cm) were expected in the Keys and western portions of Florida through Wednesday, which may result in considerable flash and urban flooding, along with minor to isolated moderate river flooding.

A few tornadoes were possible across south Florida on Monday night and across the Florida peninsula on Tuesday, the agency added.

"All Floridians should prepare for the possibility of heavy rain, flooding and potential power outages," Florida Governor Ron DeSantis wrote on Twitter.

In Seminole, Florida, residents filled sand bags and placed them outside their homes to prevent flooding.

"If we have a lot of water .. and I wait till later to get sand bags there won't be any left, and then I will have a wet bedroom," said Wendy Schultz, adding she would stock them anyway for the rest of the season "'cause, you know, it's Florida."

Authorities and locals in some Caribbean island nations including Cuba had already started work by Monday on repairing damage caused by Elsa such as removing toppled trees and other debris and restoring power.