The rain battered the parishes around Baton Rouge and is expected to move west, he said at a news conference Saturday.
There are record levels of flooding and cresting along rivers and creeks that will affect homes, roads and driveways, he said.
"This is a major disaster," the governor said. "This is an ongoing event and we are still in the response mode."
At least three people have died so far as a result of the flooding sweeping through south Louisiana, officials said.
The body of a 30-year-old woman was recovered Saturday afternoon in St. Helena Parish, Michael Martin, the chief of operations for St. Helena Parish Sheriff's Office, said The woman was traveling with her husband and mother when their vehicle was swept away by the flood. Her mother and husband were rescued.
Officials have not released the name of the woman.
She is the second known flood victim in St. Helena Parish. Samuel Muse, 54, of Greensburg died when his vehicle was submerged Friday after a portion of Highway 10 collapsed at Darlings Creek, CNN-affiliate WAFB reported.
"At this time, troopers believe that Muse attempted to drive through high water and his vehicle was swept off the road," the Louisiana State Police said.
The state's first flood-related fatality happened in East Baton Rouge Parish on Friday. A 68-year-old man drowned when he slipped and fell in flood water.\
There was almost a fourth victim, but three men in a boat stumbled on the woman's nearly submerged convertible just in time, and struggled to pull her out as the car filled with water.
"Oh my God, I'm drowning, I'm drowning," the woman said in a faint voice, as captured in a video given to CNN.
"We're coming, we're coming," one of the men said. They tried to smash the passenger side window.
"Please help me," the woman said.
One man asked for a knife to cut the soft top and hopped on the trunk of the car, which was still sticking in the air with the rest of the car nose-dived into water, quickly sinking.
As the underwater car started to float away under his weight, the man jumped into the water, frantically ripping at the soft top to no avail; then he reached in the car's driver-side window, trying to reach the victim.
Just when it looked like she was lost, the woman stuck her arms out of the water toward him. He got a good hold and pulled her to safety.
She popped up through the water and announced they needed to rescue one more victim.
"Get my dog, get my dog,'' she said, her frantic voice, choked with water. "Get my dog, now. I'll go down."
"I can't get the dog," he said, as he felt inside the submerged convertible.
He ducked under the water to reach into the car.
"Maybe she's gone," said one of the men in the boat.
"No -- she better not be," the woman said, her voice strained.
The rescuer reemerged and exhorted: "I got your dog."
He held up the small, white, terrier-looking creature, turned to the victim and in a calmer, more exhausted but happy voice said: "Swim for the boat."
National Guard soldiers, search assets deployed
More than 1,000 people have been rescued from cars, homes and elsewhere from swift-moving floodwaters and more than 100 pets have been saved, Edwards said.
"People that should have evacuated didn't, so they are having to be evacuated," Gov. Edwards said.
Ray Cutrer told CNN that the flood seemed to come out of nowhere after about 21 inches of rain fell over 24 hours. His daughter, whom he had moved next door to two years ago, believed they might get a bit of water in the house but didn't fear a deluge.
"Our guard was down," he said. "And then it was a matter of just watching the water continually rise."
By midnight Friday they were storing furniture and other valuables in the attic and carrying what they could over the back property line as water continued to fill the road.
Saturday, when they returned, Cutrer found his house had escaped damage but his daughter's was devastated.
She and her husband will be living with him and his wife until repairs are done, he said, while another washed-out neighbor is staying with Cutrer's brother.
"We're just keeping them right here in the neighborhood, and we are all going to be working right here with them, cleaning it out," Cutrer said. "That is the way we can give back to this community."
He added, "I promised God when I saw my house didn't have any water in it, I said, 'Lord, I will be here to help the ones who did,' and I am. I will be right here. We'll help them every way that we can."
He said the fire department had to rescue neighbors by boat.
The governor has also deployed the Louisiana National Guard, which said it has approximately 1,000 soldiers on the ground assisting in search and rescue, that number will increase to 1,200 to 1,250 by the end of the day Saturday.
Also deployed were 170 high water vehicles, 20 boats, and five helicopters.
At least 18 parishes have declared emergencies, the governor said, with three in the process of doing so.
This is in addition to the state of emergency Edwards declared Friday. It remains in effect until September 10.
He said people living in areas where they've been asked to evacuate should heed warnings and people should stay off the road.
About 16 shelters are open. Power outages have been reported and roads, including portions of Interstate 10 and others, have been closed. There are more than100 roads closed throughout the state.
The Red Cross is already distributing food and water to shelters.
The state is preparing to ask for federal help in recovery efforts when it determines damage estimates but for now, the governor said, it and the parishes are handling the response efforts.
Water got into the governor's mansion, and Edwards said the electricity has been turned off as a precaution. The office moved its operations to a state police facility farther north.
James Waskom, director of the governor's office of homeland security and emergency preparedness, also briefed reporters Saturday.
The round-the-clock vigilance of rescue teams and police played out Saturday in parishes across central and southern Louisiana, from the Mississippi to Texas borders.
One example of such activity was Livingston Parish, near Baton Rouge..
As the rain pounded the Bend Road area of the drenched parish early Saturday, Livingston sheriff's deputies worked to get the word out to several hundred people along that stretch: Get out now if you can.
This is a "life-threatening situation," sheriff's office spokeswoman Lori Steele said in a TV interview.
She gave instructions to people on where to meet deputies who can transport them to shelters. The department went into action on social media to inform people what to do.
"Our main goal is no loss of life."
Livingston Parish President Layton Ricks issued a warning about the Amite River corridor.
"The Amite River is continuing to rise at a rapid rate and will continue to do so. If you live on the Amite River corridor it is urgent that you make plans to evacuate your home immediately," he said.
The National Weather Service
offices in New Orleans and Lake Charles issued flash flood warnings Saturday morning for portions of several parishes, and heavy rain was reported.
Rain in some spots was beginning to diminish during the day.
"Excessive runoff from heavy rainfall will cause flooding of small creeks and streams," the Lake Charles office said.
The New Orleans office said "life-threatening flooding is occurring over a large area."
"This is a particularly dangerous situation. Seek higher ground now."
No break in the rain for a while
CNN meteorologist Derek Van Dam said Baton Rouge received twice the amount of rain in one 24-hour period than it normally receives in the entire month of August. The average for August is 5.82 inches, he said.
Some rainfall totals have exceeded 20 inches. Livingston has received 21.29 inches from late Thursday until early Saturday, he said.
One river, the Tickfaw, rose 20 feet in 14 hours, breaking a previous crest record by more than three feet, he said. He said other rivers are reaching record flood stages.
"The heaviest rain is behind us," Van Dam said. "I don't see any break in the weather until early in the week next week. The rain will continue and ease by Tuesday.
The ground is extremely saturated, he said, and any additional rainfall is going to cause more flooding. He said the moisture is going to spread east and north into the Ohio River Valley.
In Livingston, the sheriff's office had to move its 911 communications center to another location -- the emergency operations center in the parish government building -- because it was taking on water, the parish sheriff's office said in a statement..
"For hours, deputies have been handling an extremely high call volume and have been able to keep floodwaters at bay. Unfortunately, the floodwaters have proved to be too much," the statement said. There's been "no interruption in services."
Louisiana State University in Baton Rouge announced that the school is closed. It said in tweets that campus streets were impacted by water.
"Please stay away from campus if possible," the school tweeted. LSU "Football Fan Day and Media Day"
on Sunday are canceled.
"Never seen water like this"
Todd Voight, 31, who lives behind Brandon's Appliances in Amite, checked on his home and the store he runs with his brother Brandon.
Both took on water, but were not severely damaged. "I've never seen water like this," said the lifelong Amite resident.
Sandy Morgan, 34, was rescued by boat Friday night along with his family and returned home Saturday morning to survey the damage.
He told CNN he built the home six years ago, and only got flood insurance six months ago.
"Thank God," he said.