The hurricane, which formed east of the Caribbean's Leeward Islands on Saturday, is expected to become stronger as it moves northwest.The forecast says Irene is set to move off the north coast of Puerto Rico on Monday morning before travelling near or over the northern coastal regions of the Dominican Republic later in the day. The Florida Keys islands could also be on the forecast track.
Puerto Rico, the US Virgin Islands, the British Virgin Islands, Barbados, Curacao, Antigua and Barbuda have issued tropical storm warnings.
Other Caribbean islands were also affected by the warnings, including Saba, St. Eustatius, St. Martin, Dominica, St. Kitts and Nevis, Antigua, Anguilla and Montserrat.
It is too early to determine whether the storm could threaten US oil and gas installations in the Gulf of Mexico.
Meanwhile, US forecasters say the Atlantic hurricane season looks to be more intense than first predicted.
Gerry Bell, the lead hurricane season forecaster at the National Weather Service, says the region was "primed for high hurricane activity" from August through October, with more intense storms than those seen so far.
Experts now predict the formation of 14 to19 named tropical storms, of which seven to 10 could become hurricanes, during the season which officially runs from 1 June 1 to 30 November.
Three to five of those hurricanes could be "major" or at least a category three on the five-level Saffir-Simpson hurricane wind scale, meaning sustained winds of at least 179 kilometers per hour, said Bell.
In May, US forecasters had predicted a total of 12 to18 named storms, with six to 10 hurricanes.
With a total of 12 hurricanes, the 2010 season left hundreds dead in floods and mudslides in Central America and the Caribbean, where they destroyed homes and infrastructure and devastated crops.