Tropical Storm Isaac is expected to produce total rainfall accumulations of 2 to 4 inches with isolated amounts up to 8 to 10 inches over Dominica.
Officials were warning residents in the Cayman Islands to keep monitoring Tropical Storm Isaac Friday evening, after the unpredictable cyclone regained strength.
Isaac is becoming less organized over the Eastern Caribbean Sea according to the U.S. National Hurricane Centre.
Forecasters say it is especially risky after dark because people trying to escape may not realize how deep flood water is on roads.
A tropical storm may form off the Texas Gulf Coast by Friday, bringing heavy rains to areas already drenched in the past few weeks, USA government and private forecasters said on Tuesday.
The turbulent weather is coming off the back of one of number of major storms now raging in the Atlantic, another of which, Hurricane Florence, has caused mass evacuations on the east coast of United States this week.
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National Weather Service officials in Honolulu urged residents to remain careful, noting that the difference between a Category 1 hurricane and a tropical storm is just 5 miles per hour wind speed. A small-craft Warning means in this case that surface winds greater than or equal to 25 knots and seas equal to or greater than 3m (10ft) are already affecting or expected to affect the marine area.
Less rain is predicted for St. Thomas, St. John and Water Island.
Road and bridges may close, with fallen trees are expected.
Airlines cancelled more than 2,100 flights through Sunday.
In New Bern, population 29,000, flooding on the Neuse River left 500 people in peril.
"The wind was so hard, the waters were so hard ..." She retreated and was eventually rescued by a boat crew; 140 more awaited assistance. "I love hurricanes. But this one has been an experience for me", she said.