Turks and Caicos could experience up to 20cm of rainfall and life-threatening flash flooding from the storm, which was just offshore of the chain's biggest island, the National Hurricane Center said in its morning update.

A tropical storm warning is up for the southeastern Bahamas and concern is growing that the hurricane could have Bermuda in its sights.

Fiona, the first "major hurricane" of the season, is forecast to grow into a Category 4 in the coming days as it turns north and passes near Bermuda later this week, NHC senior hurricane specialist Richard Pasch said.

"Turks and Caicos Islands, I urge you to heed the advice and warnings given by the Department of Disaster Management and Emergencies and implore you to carry out all necessary preparations to protect your families and your property," Premier Washington Misick said in a statement from London, where he was attending the funeral of Queen Elizabeth II.

At least three people have died in the storm, two in Puerto Rico and one in Guadeloupe earlier in the week, officials said.

On the Turks and Caicos Islands, a British Overseas Territory with 40 low-lying coral islands and a population of about 40,000, the government's National Emergency Operations Centre (NEOC) told residents of three eastern islands to shelter in place and ordered businesses to close.

"All persons are to remain indoors at their residence, place of safety or where they seek shelter until the NEOC issues NATIONAL ALL CLEAR", the agency told residents of Grand Turk, South Caicos and Salt Cay.

Residents were stocking up on food and water while shelters were being prepared.

Foreign governments issued travel alerts for the islands, a popular tourist destination.

Similar preparations were under way in the eastern Bahamas.

Fiona is on track to hit the eastern Bahamas on Wednesday, when it could reach Category 4 strength.

Australian Associated Press