Elsa batters Cuba as it approaches Florida with increased intensity

After battering Cuba with a dangerous storm surge, mudslides and "flooding rains," Tropical Storm Elsa has gained slightly in intensity as it headed north toward the Florida Keys, the US National Hurricane Center reported.

The storm left a trail of destruction through the Caribbean, claiming at least three lives.

But Florida appeared to be getting a bit of a break, as forecasters shifted its likely path westward, suggesting not the direct hit earlier expected but more a glancing blow to the southwest coast of the state.

In Surfside, on Florida's east coast, workers overnight used explosives in the controlled demolition of the still-standing portion of a collapsed condo building. The job was accelerated for fear Elsa might topple the structure in uncontrolled fashion.

But on Monday, Miami-Dade County Mayor Daniella Levine Cava told CNN that officials were "very hopeful" that, with Elsa's current path, they would not now have to pause search-and-rescue efforts.

READ MORE: Collapsed Florida apartment block completely demolished ahead of storm

Storm approaches Florida

The storm is expected next to approach the Florida Keys  — the archipelago at the state's southern tip  — sometime Tuesday on its march northward.

The National Hurricane Center, in a 2:00 pm update (1800 GMT), said Elsa had maximum sustained winds of 65 miles per hour (100 kilometres per hour). 

It was moving northwest at 14 miles per hour.

Cuba's meteorological institute Insmet reported earlier that Elsa had cut through the island with winds of up to 100 kilometers an hour, with "some stronger gusts."

States of alarm were sounded in the provinces of Havana, Mayabeque and Artemisa.

The storm was expected to dump up to 38 centimetres (15 inches) of rain in parts of Cuba, the NHC said.

READ MORE: Tropical Storm Elsa wreaks havoc as it tears through the Caribbean

Earliest fifth named storm

During its earlier approach through the Caribbean, Elsa claimed two lives in the Dominican Republic and a third in the island state of Santa Lucia, the Caribbean Disaster Emergency Management Agency (CDEMA) said.

While Elsa ravaged the southern coast of Cuba from Sunday until Monday morning, no major damage was reported.

Cuban President Miguel Diaz-Canel said late Sunday on Twitter that there had only been damage to farm crops.

On Friday, Elsa became the first hurricane of the Atlantic season before weakening to tropical storm status on Saturday.

Elsa's advent represented the earliest ever that a fifth named storm has struck the region. 

Typically, the fifth named storm does not arrive before August.

READ MORE: Hurricane Elsa falls back to tropical storm as it batters Haiti