Tropical storm Eta brought strong winds and torrential rain to Cuba on Sunday after having earlier cut a destructive and deadly path through parts of Central America and southern Mexico.

The storm was expected to turn toward Florida later and strengthen, with the US National Hurricane Center saying it was "forecast to be near hurricane strength when it moves near or over the Florida Keys."

Cuba's meteorology institute Insmet said Eta made landfall at 4:30 am (0930 GMT) on the border between the central provinces of Sancti Spiritus and Ciego de Avila.

Its maximum sustained winds were around 100 kilometers per hour (about 60 miles per hour) with higher gusts, the institute said.

A tropical storm is considered a hurricane when it hits wind speeds of 74 miles per hour.

Heavy rains were reported in the eastern half of Cuba, where authorities have evacuated thousands of people due to the risk of flooding.

Insmet said that high winds were expected to produce strong swells and rising sea levels on the southern coast.

It added that Eta would continue crossing over the province of Ciego de Avila before passing through the north coast and turning northwest toward Florida.

Aerial view of a mudslide caused by Eta and where it is estimated that dozens of people died in the village of Queja, in San Cristobal Verapaz, Guatemala on November 7, 2020
Aerial view of a mudslide caused by Eta and where it is estimated that dozens of people died in the village of Queja, in San Cristobal Verapaz, Guatemala on November 7, 2020 POOL / Esteban BIBA

Florida Governor Ron DeSantis declared a state of emergency in the state's southern counties on Saturday in advance of the storm, even as residents in the rain either protested or celebrated Joe Biden's win in the US presidential election.

The Florida Keys will close schools on Monday, Covid-19 testing sites were temporarily shut and authorities opened shelters and began handing out sandbags for residents to protect their homes from flooding.

Eta hit Nicaragua on Tuesday as a powerful hurricane before losing strength.

It caused torrential rains that have left some 200 victims dead or missing in Central America.

The most affected country has been Guatemala, where about 150 people are missing.

Rescuers on Saturday searched for the bodies of residents of an indigenous village in the north of the country that was hit by a landslide.

In Honduras, heavy flooding in the north and northwest of the country killed 23 people, according to authorities.

Torrential rain and a bitter cold front linked to Eta have also claimed at least 20 lives in the southern Mexican state of Chiapas.

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