Authorities said Monday at least seven deaths had been blamed on the storm, MSNBC reported.
At 11 p.m. EDT the storm was centered about 20 miles southwest of Alexandria, La., and was moving toward the northwest at about 13 mph with maximum sustained winds of about 60 mph with higher gusts.
The storm was likely to continue moving on that track with a decrease in forward speed into Tuesday, and to cross western Louisiana Monday night and reach northeastern Texas Tuesday. Gustav is likely to be downgraded to a tropical depression Tuesday, forecasters said.
A few tornadoes were possible in the lower Mississippi Valley and the central Gulf Coast Monday night and early Tuesday.
Louisiana officials said Monday the Caernarvon Mississippi River diversion in Plaquemines Parish would be opened to take pressure off a levee that was being overtopped -- but not breached -- in Braithwaite, near the St. Bernard Parish line, the Times-Picayune of New Orleans reported. Floodwaters spilled over the top of the levee, threatening the Braithwaite Park subdivision, the newspaper said.
The U.S. Army Corps of Engineers said flooding in New Orleans' Upper Ninth Ward doesn't pose a danger. Up to six inches of flooding had been reported in the beleaguered area from water spilling over the western side of the Industrial Canal floodwall, Times-Picayune said.
A hurricane warning remains in effect from just east of Cameron Island, La., to the Mississippi-Alabama border, including New Orleans and Lake Pontchartrain. A tropical storm warning was in effect from Cameron westward to just east of High Island, Texas, and from the Mississippi-Alabama border to the Florida-Alabama border.
A storm surge of 10-14 feet above normal tide levels was expected near and to the east of where Gustav's center crosses the coast, the hurricane center said.
Gustav was expected to produce a total rainfall of up to a foot over portions of Louisiana, Mississippi, Arkansas and Texas, and also could spark a few tornadoes over the central Gulf Coast, the center said.
The storm killed more than 90 people in Haiti, Dominican Republic and Cuba before it entered the Gulf of Mexico during the weekend.