NEW ORLEANS — Widespread flooding in Louisiana and Mississippi has damaged thousands of homes, and the risk of rising water prompted additional evacuations Sunday.

At least four deaths have been reported in Louisiana amid the flooding that began last week, and the National Guard has rescued nearly 3,300 residents. Two fishermen have been missing for days in Mississippi.

Flood warnings were in effect across the region as many rivers remained dangerously high. Also of concern was another line of thunderstorms that hit parts of Oklahoma, Arkansas, northern Louisiana and northern Mississippi on Sunday night, bringing more rain and reports of tornadoes in Arkansas.

“At this point, any rain will aggravate the flooding situation,” Davyon Hill, a meteorologist with the National Weather Service in Shreveport, said.

Downpours — part of a system that affected Louisiana, Mississippi, Arkansas, Tennessee and Alabama — have submerged roads and cars, washed out bridges and forced residents to flee homes.

In Louisiana, emergency officials said more than 4,958 homes were damaged. That number is expected to rise as more reports come in from areas still battling floodwaters. Mississippi reported that 185 homes were damaged by floodwaters and about 650 homes sustained minor damage.

On Sunday, President Barack Obama signed an order declaring the flooding in Louisiana a major disaster. The president’s declaration triggers federal aid for flood victims.

Louisiana Lt. Gov. Billy Nungesser said he was worried that many flood victims had not purchased flood insurance.

“A lot of these people I spoke to did not have flood insurance because they had never flooded before,” Nungesser said in a telephone interview.

He warned that residents may not get federal disaster aid if they didn’t have insurance. “It’s not going to be the open check book,” he added.

Authorities in Louisiana’s Natchitoches Parish said Harold Worsham, 78, drowned while trying to flee floodwaters on Saline Bayou.