Flooded homes along the Tangipahoa River near Amite, Independence, Tickfaw and Robert, La. (Ted Jackson/Nola.com/Times-Picayune via AP)

Historic flooding in Louisiana forced thousands from their homes and left at least six people dead, authorities said, with officials warning that the flood’s impact is far from over.

“Obviously, this remains a very serious event … and it remains ongoing,” Gov. John Bel Edwards (D) said during a news briefing late Sunday night. “This truly is a storm that has ravaged all of south Louisiana.”

More than 20,000 people were rescued from their homes through Sunday night, Edwards said during the briefing. The governor also said more than 10,000 people had been brought to shelters in southern Louisiana, most of them in the Baton Rouge region.

“We are going to get through this,” Edwards said, adding: “We have a lot of work ahead of us.”

In a message Monday, Edwards said that even though the sun may have come out in some areas, it was not clear when floodwater would recede.

“This is not the time to let our guards down,” he said in a statement. “We need to keep people off the streets as much as possible – do not go out sightseeing.”

There were six storm-related deaths confirmed by Monday afternoon, said Devin D. George, state registrar of vital records.

One man died after falling into a ditch while being helped through floodwater, while a woman who was riding in a truck was swept away by floodwater.

The flooding dramatically impacted scores of people across Louisiana, forcing families to flee to safe ground and stranding people on waterlogged interstates.

Government offices in more than two dozen parishes across the state were shuttered Monday, and the same offices were also going to be closed Tuesday, officials said.

Hundreds of state roads were closed because of high water. Scores of shelters were opened across Louisiana, with the largest number in East Baton Rouge Parish, the state’s biggest parish with more than 446,000 residents. Louisiana State University in Baton Rouge closed its campus again Monday and canceled freshman orientation.

On Sunday, the Louisiana State Police had worked to rescue people from hundreds of cars stranded on Interstate 12 just east of Baton Rouge, the state capital:

Edwards declared a state of emergency for all of Louisiana on Friday, and by Sunday he asked President Obama to declare the flooding a major disaster to open up access to federal funding.

“I have traveled to affected areas and have seen the destruction caused by this unprecedented flooding,” Edwards said in a statement on Sunday. He added: “This is an ongoing event, and we are confident that every available state and federal resource will be brought to bear.”

Obama on Sunday signed a disaster declaration for New Orleans, which makes federal funding available for people in four parishes: East Baton Rouge, Livingston, St. Helena and Tangipahoa. The White House said that Obama was briefed about the flooding by Lisa Monaco, his adviser for homeland security.

Edwards said that he expected more parishes would be “added to the declaration on a rolling basis.” The federal funds can help with home repairs, temporary housing and property losses.

By Monday morning, Edwards’s office said that 11,000 people had registered for Federal Emergency Management Agency assistance, most of them from parishes listed in Obama’s declaration.

Preliminary data from the National Weather Service said that in some parts of Louisiana, as much as 26 inches of rain fell. The rainfall at several reporting stations broke records, the agency said, as did the cresting rivers at various locations.

The U.S. Coast Guard said its crews had rescued dozens of people from Baton Rouge during the flooding, picking them up from rooftops, cars and trailers. In video footage posted online, a Coast Guard crew air-lifted people from a flooded area where the water was reaching the tops of buildings.

This flooding was caused by two weather-related features: extreme humidity and near-stationary low pressure that hovered over the Gulf Coast for days. There were also incredible numbers measured for precipitable water — or how much moisture is in the air at any given time. In a statement issued Thursday, the National Weather Service noted that the amount of moisture in the atmosphere was “astoundingly high.”

When Damien Callais, a New Orleans native, heard reports that floodwaters were trapping people, he jumped in his car and raced into Baton Rouge. Callais began mobilizing all the volunteers that wanted to help — fishermen with boats, locals who knew back roads and dirt paths, residents who simply wanted to do something to help save their neighbors. He called it the Cajun Navy.

“It’s insane,” he said as he prepared to hop on another boat. “It’s crazy how many people are willing to drive from anywhere to help.”

In the past 24 hours, Callais said he and others have pulled newborns, the elderly, even a woman who had just had neck surgery out of the floodwater. He said they rescued people stuck on roofs and those swimming with their dogs, trying desperately to keep their pets’ heads above water.

Joshua Lawrence said he and his family have been stranded since Saturday when they fled their home in Denham Springs, east of Baton Rouge. They took refuge in the clubhouse of a subdivision on higher ground, and have been knocking on strangers’ doors in search of food and water.

“We are on our last leg, to be honest with you,” said Lawrence, 30, speaking by phone Monday afternoon. “We haven’t had food or anything to drink all day today.”

He said his children — ages, 2, 4 and 12 — were tired, hot and confused. “They can’t understand why we can’t go home,” he said.

His mother, Karen Fornea, said she had been calling, texting and posting on Facebook nonstop for days in an effort to organize a rescue, but no one has come.

Fornea said some would-be rescuers in boats told her they had been turned back by state officials who were trying to control the area. Lawrence, who works as a manager at a casino, left his overnight shift early Saturday morning after his wife called to tell him that water was rising fast.

They stashed their belongings as high as they could and then left in their Jeep Patriot, headed for Lawrence’s mother’s house in La Place, normally a little over an hour away. But in every direction, roads were shut down.

“There was no way out,” Lawrence said.

They tried a church shelter, but hundreds of people there and there were no pillows or blankets, and there seemed to be little food, he said. They took refuge Saturday night in the clubhouse of a subdivision that seemed to be safe from the rising water. On Sunday night, they slept in the Jeep after being told about a group with guns roaming the neighborhood in search of food and water.

They have run out of diapers, Lawrence said, and the toddlers were crying.

“This is the worst situation I’ve ever been through,” he said.

Angela Fritz in Washington and Sarah Netter in Slidell, La., contributed to this report, which has been updated since it was first published.