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More than 20,000 people in Louisiana have been rescued amid unprecedented flooding that has resulted in at least three deaths, and officials said Sunday that some rivers continued to rise.

"It is not over," Gov. Jon Bel Edwards said at a news conference. Officials believe one person may be unaccounted for, he said. His office said the federal government has declared a major disaster for the state that initially covers four parishes.

In a positive development, rainfall amounts have diminished as a slow-moving weather system edged west toward Texas, the governor said. The system dumped more than a foot of rain in some areas of Louisiana.

"Any time you break a record, the National Weather Service cannot tell you what you can expect in the way of floodwaters—how wide they're going to be, how deep they're going to be," Mr. Edwards said.

Mr. Edwards hailed the "heroic efforts" of rescuers who plucked people from inundated homes and cars. In an episode captured on video, a man jumped off a boat, ripped the roof of a convertible sports car and pulled a woman and her small dog out as the car sank.

The rescuers weren't law enforcement, just citizens who saw a need to act, said Sgt. Jared Sandifer, a state police spokesman. And they weren't alone, he said: "We have had reports of people being rescued from trees, from attics of houses, from roofs of cars."

More than 500 pets have been rescued, the governor said.

More than 10,000 are in shelters across Louisiana, mostly in the Baton Rouge area. A shortage of cots required some to sleep on the floor. "We are working as fast as we can to get you the basic comforts," said Marketa Walters, who heads the Louisiana Department of Children & Family Services.

Over 1,000 cars and trucks were stranded Saturday on parts of Interstate 12, State Police Superintendent Michael Edmonson said. By Sunday afternoon, the motorists were leaving the interstate as floodwaters receded.

AT&T Inc. said one of its switching centers that carries network traffic in the Baton Rouge area had flooded, disrupting cellphone service. Col. Edmonson of the state police urged people to use Wi-Fi to access social media and make calls over FaceTime.

Maj. Gen. Glenn Curtis of the Louisiana National Guard said the Guard deployed about 1,700 soldiers to help with the rescue effort.

Though heavy rainfall had ended in hard-hit southeast and south-central Louisiana, the scattered showers and storms expected for the next week pose a flooding risk because of ground saturation, said National Weather Service meteorologist Danielle Manning.

"It's not going to take a whole lot of rain to exacerbate some of the problems," she said.

The weather system that caused the flooding began dumping heavy rain on the region late Thursday. The town of Livingston, 25 miles east of Baton Rouge, saw a three-day total of 25.5 inches of rain, most of which fell in two days, Ms. Manning said.

The Amite River in southeast Louisiana was continuing to rise Sunday as the crest moved south. "It's not just that it's at a record level, it's feet above the previous level," Ms. Manning said. Water has been "back-feeding" into the streams and bayous that feed the river, she added.

Write to Scott Calvert at scott.calvert@wsj.com

(END) Dow Jones Newswires

August 15, 2016 13:15 ET (17:15 GMT)

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