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New Orleans (CNN) -- Slow-moving Tropical Storm Lee churned toward the Gulf Coast Saturday, dumping heavy rains over the southern parts of Louisiana, Mississippi and Alabama.
At one point, approximately 38,000 customers in Louisiana had lost power because of the storm, but that figure was cut to less than 12,000, Entergy reported.
Lee, which is lumbering north-northwest at 4 miles per hour, is expected to cross the Louisiana coast Saturday evening and then move slowly across the southern part of the state on Sunday.
"We have severe weather warnings and tornado warnings in effect for parts of the state and residents everywhere need to use extreme caution," Louisiana Gov. Bobby Jindal said. "Tropical Storm Lee is moving slowly, as expected, and we are already seeing flooded roads and other effects from rising water levels throughout South Louisiana."
The governor deployed National Guard liaisons to two of the state's parishes to help with emergencies.
Heavy rains will pound some areas along the Gulf coast, with parts forecast to receive up to 20 inches.
The National Hurricane Center said that "a few tornadoes will be possible" through Saturday night over portions of southern Louisiana, Mississippi and Alabama as well as the far western Florida panhandle.
A tropical storm warning is in effect from Destin, Florida, all the way to Sabine Pass, Texas.
"This storm is moving painfully slow," New Orleans Mayor Mitch Landrieu told reporters, during a break in the storm. "We have to be vigilant."
Jindal said 10 parishes have issued emergency declarations. He urged residents to pay attention to the weather and flash flooding warnings.
In New Orleans, much of which sits below sea level, Landrieu took similar measures. The storm will test the levees rebuilt after Hurricane Katrina pounded the region six years ago this week.
The city is likely to see heavy rain in the next few days, according to Landrieu. He declared a state of emergency and urged residents to "prepare for the worst ... hope for the best."
A mandatory evacuation was ordered for several towns in Jefferson Parish.
CNN iReporter Andrew Kaile shot video of flooding in Metairie, Louisiana, where water filled the street outside his home.
"We are a sturdy people. All Gulf Coasters are willing and able to weather any storm," he wrote.
Tropical Storm Lee comes about a week after Hurricane Irene pounded the East Coast, killing more than 40 people and leaving millions without power.
The slow-moving storm was located about 50 miles southwest of Morgan City, Louisiana, the Hurricane Center said Saturday evening. After gaining strength earlier in the day, its maximum sustained winds decreased to 50 mph.
Gradual weakening is forecast to occur Sunday and Monday.
Parts of southern Louisiana, Mississippi and Alabama could see 10 to 15 inches of rain through Sunday night, with isolated totals of up to 20 inches, forecasters said.
In Alabama, officials shut the Port of Mobile on account of rough seas.
Some energy producers evacuated employees ahead of the storm. About 60% of oil production in the Gulf and more than half of natural gas production have been shut down, according to the Bureau of Ocean Energy Management, Regulation and Enforcement.
In Biloxi, Mississippi, public works crews worked to clean storm drains and catch basins on streets prone to flooding ahead of the expected storm.
"This will be an extreme multiday rain event, and there will be issues with localized flooding," said Sgt. Milton Houseman, the city's emergency manager. "The good news is that, at this time, with the projections we've seen, we don't expect any issues with river flooding, because the rivers are low."
In addition to expected flooding and storm surge, the weather is threatening to ruin Labor Day weekend for thousands of beach-goers.
As of Saturday afternoon, it was unclear whether Katia, a tropical storm swirling in the Atlantic, would endanger the United States.
CNN's Dana Ford, Joe Sutton, Dave Alsup and Vivian Kuo contributed to this report.