The U.S. National Hurricane Center warns isolated tornadoes are also possible Sunday over portions of the Keys and central and southern Florida.
Isaac's maximum sustained winds have increased to 100 kilometers per hour with higher gusts.
A hurricane watch has been issued from the mouth of of the Mississippi River eastward to Indian Pass, Florida. The watch area does not include metropolitan New Orleans, where Hurricane Katrina left thousands homeless in 2005.
Isaac battered eastern Cuba Saturday, after killing at least four people in Haiti, which is still recovering from a devastating 2010 earthquake. There were no reports of fatalities in Cuba.
The threat of the storm has caused the U.S. Republican Party to postpone the start of most events at its national convention in Tampa, Florida from Monday to Tuesday afternoon.
Protesters who have set up camp in Tampa, dubbed "Romneyville," near the site of the Republican convention will likely need to temporarily abandon their outdoor accommodations.
