BATON ROUGE, Louisiana — Search-and-rescue operations were still underway Tuesday in Louisiana, where at least 11 people have died in severe floods that have damaged about 40,000 homes, state officials said.

Emergency crews had already plucked more than 20,000 people and 1,000 pets from flooded areas after a storm that broke records for 24-hour rainfall in multiple locations, Gov. John Bel Edwards told reporters.

Rain-swollen rivers are receding in much of the state, but state officials warned of remaining dangers. Some communities in southern Louisiana could see waters crest later in the week, according to national forecasters.

More than 8,000 people slept in emergency shelters on Monday night, unable to return to their homes, Edwards told a news conference. The state planned to impose curfews on Tuesday night in the parishes with widespread damage.

“This is a historic flooding event,” Edwards said. “It’s unprecedented.”

The storm dumped more than 2½ feet of rain near Watson, Louisiana, from Thursday to Monday morning, the highest total reported, according to the National Weather Service.

In Abbeville, Louisiana, a 125-year-old record for 24-hour rainfall was shattered with 16.38 inches reported from Friday to Saturday, the weather service reported.

Three Maine Red Cross volunteers are in the region assisting with the disaster relief efforts. Margaret Rode of Tenants Harbor, a five-year Disaster Mental Health Services volunteer with the Red Cross, is providing emotional support and helping those cope with the devastating loss of their belongings and/or loved ones.

Sharon Collin of Cumberland Foreside, an 11-year Red Cross in Maine volunteer, has been deployed to disaster incidents in California, Texas, Oregon, Washington and participated in the response during Hurricane Katrina and at the Boston Marathon bombing.

Todd Tisdale of Farmington, a two-year volunteer with the organization has previously been deployed to Texas to assist during the historic flooding in June.

In some water-ravaged areas, houses flooded to rooflines, and coffins floated away from cemeteries. Motorists were trapped on highways. President Barack Obama issued a disaster declaration Sunday, with a total of 20 parishes approved by Tuesday for federal assistance.

Already, 40,000 residents have registered for disaster aid, Edwards said.

In hard-hit Denham Springs, residents were gutting waterlogged homes, dumping soaked carpets and mattresses.

Sonya Mayeux was still in disbelief. On Saturday, she awoke at 9 a.m. to rising, knee-deep water in her backyard. By 11:30 a.m., the water was nearly above her white SUV.

A neighbor rescued her family by boat. Ultimately, her house flooded nearly to the roof.

“The water just came up so fast,” she said.

Craig Fugate, head of the Federal Emergency Management Agency, told reporters the “very large disaster” was affecting more people than flooding in March that left at least four dead and thousands of homes damaged in Louisiana and Mississippi.

Louisiana will mark the 11th anniversary this month of Hurricane Katrina, which killed more than 1,800 people when floods overwhelmed levees and broke through flood walls protecting New Orleans on Aug. 29, 2005.

Louisiana’s confirmed death toll from the latest flooding rose to 11 on Tuesday, the state Health Department said. By parish, it reported five fatalities in East Baton Rouge, three in Tangipahoa, two in St. Helena, and one in Rapides.

Among those killed was Bill Borne, the founder and former chief executive of Amedisys Inc, a provider of home health and hospice care. Officials said he drowned near his home in East Baton Rouge Parish.