With massive floodwaters receding in Louisiana, officials in the southern US state grappled Thursday with the next stage of the disaster response -- how to help affected residents recover.

Officials continued to search tens of thousands of homes and countless cars for victims and survivors of the severe flooding that began Friday after heavy rains.

The death toll climbed to 13, officials said.

More than 86,000 people have registered for US government emergency assistance.

US Secretary of Homeland Security Jeh Johnson, who is in charge of the department that will dole out the aid, visited areas affected by the historic flooding and met with local officials to discuss the nascent recovery effort.

"I will be briefing the president on the situation that I see here at some point very soon," Johnson told a news conference, adding that President Barack Obama has been receiving daily briefings about the ongoing emergency.

The Federal Emergency Management Agency, which reports to Johnson, began Thursday to assess the estimated 40,000 homes that were affected by floodwaters. Some people could receive financial assistance in as soon as 48 hours, Louisiana Governor John Bel Edwards said.

"We are working again today to formulate a more complete plan for transitioning from response to recovery," Edwards said, noting the urgent need for temporary housing.

Some areas of southern Louisiana do not have enough hotel rooms and rentals, he said.

Meanwhile, more residents were leaving shelters and heading home to begin the cleanup process. Overnight, shelters housed 8,000 people and by midday Thursday that number had dropped to about 4,000, officials said.

Many people were gutting their homes, ripping out drywall and insulation and removing furniture, light fixtures and appliances.

Gail McGovern, the president of the American Red Cross who called the scale of the disaster "absolutely enormous," cautioned residents to be careful of electrical fires -- known to be the next hazard following flooding.

The relief agency will begin fanning out into neighborhoods, distributing items such as pails, mops and bleach, along with food and water, she said.

"It's very important that you clean out your homes, and as soon as possible restore electricity and air conditioning, to make sure that you don't suffer mold contamination," Edwards said, addressing Louisiana residents.

Electricity was restored to most of the 40,000 customers that lost power, though 7,800 remained without it.

While many areas were drying out, the National Weather Service forecast that all waterways would not fall below flood stage until Friday.

"We are certainly not out of the woods," Edwards cautioned. "We still have floodwaters. And in fact, in some cases, record floodwaters as they move south."

Twenty-two of the state's 64 parishes, Louisiana's equivalent to counties, have been declared disaster areas.