Waves of intense weather were moving east on Wednesday, bringing flash flooding and tornadoes the New Orleans area and other parts of the central Gulf Coast, the National Weather Service said.

More than a dozen flash flood warnings were issued early in the day, including one for New Orleans where between one-half and two inches of rain have fallen and one to three inches are possible, forecasters said.

There’s also a substantial risk of tornadoes in the area, and some of those could be strong. The first tornado warnings have been issued for some rural areas, and more were expected through the morning. Forecasters warned that more than seven million people across Louisiana, Mississippi and Alabama could experience extreme weather through the day.

The weather in the region began to deteriorate before dawn. The Weather Service issued more than a dozen tornado warnings and watches that covered towns from Texas to Mississippi. One of the more significant bulletins was a tornado watch issued for the southeastern portion of Louisiana north to Columbus, Miss., until the early afternoon.

(A tornado warning is an urgent alert issued after a weather forecaster spots a possible tornado on a radar or a trained spotter sees a tornado. A watch means weather conditions are favorable for one to form in an area.)

Flooding began to inundate areas in east Texas early on Wednesday. Schools were closed and roads were shut down on Wednesday through the city of Kirbyville in Jasper County, Tx., in the east of the state. The sheriff’s office said its deputies, local fire departments and emergency authorities were deployed for rescue efforts in the area around the city of more than 2,000.

In Kirbyville, Mayor Frank George sat in his truck in the central part of the city where water had risen to several feet deep in some places. Across the street from him was the flooded Central Baptist Church. Water skimmed the roof of a parked Lincoln Continental vehicle, which was almost completely submerged.

Mr. George said that since before daylight, volunteers and a swift water team were circulating in boats throughout the streets, pulling stranded people out of homes and bringing them to a shelter. There were no fatalities or reports of injuries, he said.

Many more needed to be rescued, he said, and another shelter was expected to be opened on Wednesday. “We are getting calls as the water rises and we are expecting the water to rise,” Mr. George said in an interview. We are anticipating more calls.”

The Weather Service also issued a flurry of flash flood warnings, including one for areas surrounding Jackson, Miss., that included nearly 400,000 residents.

The cluster of storms approaching the area could dump up to four inches of rain over a short period from northeast Louisiana to southwest Georgia and the Florida panhandle, forecasters predicted. The storms are also expected to produce hail and high winds through the evening.

“Residents and visitors are advised to have multiple ways to receive warnings and never drive through flooded roadways,” the Weather Service said.

While the bulk of the severe weather was expected to begin in the morning hours and run through the afternoon, parts of Mississippi were already reeling from an overnight storm.

At least one tornado was reported in Raymond, Miss., just west of Jackson, the state capital, according to a local news outlet. Multiple trees and power lines were reported down across neighboring counties.

The National Weather Service office in New Orleans said on social media that storms moving across the city on Wednesday would approach slowly and that some of the main effects would be heavy rain and flash flooding.

In anticipation of the weather, officials closed City Hall and other city buildings Wednesday. Schools, however, remained open.

Farther north, the Weather Service office in Jackson, Miss., warned residents that damaging winds of up to 70 miles per hour would be possible on Wednesday, along with an increased chance of tornadoes, some strong, and hail.

Amanda Holpuch and Christine Hauser contributed reporting.