Much of the eastern Caribbean island of Barbados shut down on Monday as tropical storm Dorian approached the region and gathered strength, threatening to turn into a small hurricane that forecasters said could affect the northern Windward Islands and Puerto Rico in coming days.

Prime Minister Mia Mottley closed schools and government offices across Barbados as she warned people to remain indoors.

"When you're dead, you're dead," she said in a televised address late Sunday. "Stay inside and get some rest."

The U.S. National Hurricane Center issued a hurricane watch for St. Lucia and a tropical storm warning for Barbados, Martinique, St. Lucia and St. Vincent and the Grenadines. It also issued a tropical storm watch for Puerto Rico, Dominica, Grenada, Saba and St. Eustatius.

The storm was expected to dump between eight and 20 centimetres of rain in Barbados and nearby islands, with isolated amounts of 25 centimetres.

As of 8 p.m. ET Monday, the fourth tropical storm of the Atlantic hurricane season was centred about 50 kilometres east-southeast of Barbados and moving west at 22 km/h. Maximum sustained winds were at 95 km/h. Forecasters said it could brush past southwest Puerto Rico late Wednesday as a Category 1 hurricane and then strike the southeast corner of the Dominican Republic early Thursday.

<a href="https://twitter.com/hashtag/Dorian?src=hash&ref_src=twsrc%5Etfw">#Dorian</a> is expected to reach the Lesser Antilles tonight. A Tropical Storm Watch has been issued for Puerto Rico. Here are the 5 pm AST Aug 26th Key Messages. For more information visit <a href="https://t.co/tW4KeFW0gB">https://t.co/tW4KeFW0gB</a> <a href="https://t.co/mDOlekNNbs">pic.twitter.com/mDOlekNNbs</a> —@NHC_Atlantic

In St. Lucia, Prime Minister Allen Chastanet announced that everything on the island of nearly 180,000 people would shut down by 6 p.m. ET Monday, with the hurricane expected to hit around 2 a.m. ET Tuesday.

"We are expecting the worst," he said.

Some were still boarding up windows and buying food and water, but not Joannes Lamontagne, who lives in the island's southwest region. He said by phone that everything at his hotel, Serenity Escape, was already protected.

"I don't wait until it's announced," he said of the storm. "We're always prepared no matter what."

Meanwhile, in Barbados, many of the 285,000 inhabitants heeded the government's warning, including Fitz Bostic, owner of Rest Haven Beach Cottages. He said he's prepared in case officials shut down power and utility services as they have in previous storms.

"We have to be very cautious," he said in a telephone interview. "The word storm frightens me, man. I'm very nervous."

Residents board up a storefront pharmacy in Bridgetown. The prime minister of Barbados ordered schools closed and government offices closed on Monday. (Chris Brandis/The Associated Press)

In the U.S. territory of Puerto Rico, hundreds of people have been crowding into grocery stores and gas stations to prepare for Dorian, buying food, water and generators, among other supplies.

Puerto Rico Gov. Wanda Vazquez signed an executive order Monday declaring a state of emergency and provided a list of all the new equipment that public agencies have bought since Hurricane Maria.

"I want everyone to feel calm," she said. "Agency directors have prepared for the last two years. The experience of Maria has been a great lesson for everyone."

She said public schools will close Tuesday afternoon and that at least one cruise ship cancelled its trip to Puerto Rico. She said those without a proper roof can stay in one of the 360 shelters around the island.