MIAMI (Reuters) - Tropical Storm Chantal strengthened slightly on Tuesday as it swept into the eastern Caribbean and moved between the islands of Martinique and St Lucia, United States forecasters said.

Chantal was centered about 85km north-west of St Lucia, the US National Hurricane Centre said. The storm had top sustained winds of 95 kmh and was speeding west-north-west at 46 kmh.

Chantal, the third named storm of the 2013 Atlantic hurricane season, did not pose an immediate threat to US oil and gas operations in the Gulf of Mexico.

The storm is forecast to continue moving over the eastern Caribbean on Tuesday, on a path that would put it over Haiti and the Dominican Republic on Wednesday.

Forecasters said Chantal is expected to reach near hurricane strength as it approaches Hispaniola, the island made up of Haiti and the Dominican Republic, but remain a tropical storm.

Chantal could pose a particular threat to Haiti, the poorest country in the Americas, which is vulnerable to flash floods and mudslides because of its near-total deforestation.

Computer forecast models show Chantal is then forecast to move over the Bahamas, with its eye remaining well off the US coast over the weekend.

In Barbados, businesses and government officers were closed on Tuesday as the storm buffeted the island.

The authorities in the Dominican Republic issued a hurricane watch for parts of the country. Tropical storm warnings were in effect for Dominica, Martinique, Guadeloupe, Puerto Rico and the northern coast of Haiti.