(Reuters) -Tropical Storm Elsa was moving past the Florida Keys on Tuesday morning and heading toward the west coast of the state, where it was expected to make landfall on Wednesday morning after dumping heavy rain over Cuba.

The U.S. National Hurricane Center (NHC) said in a Tuesday morning advisory the center of Elsa was about 65 miles west-northwest of Key West and moving in the north-northwest direction at around 10 mph (17 kph), with maximum sustained winds of around 60 mph (95 kph).

A hurricane watch was in effect from Egmont Key, in the Tampa Bay region, to the Steinhatchee River some 180 miles north along the Gulf Coast.

“Slow strengthening is forecast through tonight, and Elsa could be near hurricane strength before it makes landfall in Florida,” the Miami-based weather forecaster said.

After a Wednesday morning landfall along Florida’s Gulf Coast, the storm is forecast to move north-northeastward across the southeast of the United States through Thursday, dropping 2-4 inches of rain across the Florida peninsula.

The arrival of tropical storm-force winds and rain was threatening to impede the search and rescue effort at the site of a condominium building collapse in Surfside, Florida, near Miami, where crews have sifted through rubble for 12 days in hopes of finding survivors. As of Tuesday morning, 32 people were confirmed dead and 113 were still unaccounted for, Miami-Dade Mayor Daniella Levine Cava said.

Tornadoes were possible on Tuesday across Florida and possible on Wednesday in north Florida, southeast Georgia and the low country of South Carolina, the NHC said.

Elsa has already killed at least three people and caused damage to infrastructure and agriculture in Caribbean islands southeast of Cuba, such as St Lucia and the Dominican Republic.

More than 100,000 people in Cuba were 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 went to government shelters, state-run media reported.

The NHC said tropical storm conditions would continue over parts of Cuba during the next several hours, with flooding possible.

(Reporting by Gabriella Borter and Maria Ponnezhath in Bengaluru; Editing by Alison Williams and Andrea Ricci)