(CNN) As the rain pounded the Bend Road area of Louisiana's drenched Livingston Parish early Saturday, 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 up with deputies who can transport them to shelters. The department's social media went into action to inform people about what to do.

"Our main goal is no loss of life."

Livingston Parish President Layton Ricks issued another 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.

State of emergency

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.

The rain that started late Thursday caused dangerous flooding that killed at least three people. It shut down highways, prompted rescues, and cut off towns.

The Louisiana State Police announced that portions of Interstate 10 in both directions near Baton Rouge are currently closed due to flooding.

Heavy rains have flooded the basement of the Louisiana governor's mansion in Baton Rouge, according to Shauna Sanford, spokeswoman for Gov. John Bel Edwards.

Edwards on Friday declared a state of emergency for all of Louisiana that remains in effect until September 10. The governor's office also worked to get information out to the public on social media.

Flash flooding

Flash flood warnings were issued by the National Weather Service offices in New Orleans and Lake Charles on Saturday morning for portions of several parishes.

The New Orleans flash flood warning said Saturday morning that "heavy rain" is falling over areas that have received 10 and 26 inches of rainfall in the past 24 hours."

"Flash flooding is already occurring," the warning said. "Additional rainfall amounts of three to six inches are possible in the warned area."

It urged people to "move to higher ground now."

Farther west in Lake Charles, the weather service warned motorists to be vigilant and said "excessive runoff from heavy rainfall will cause flooding of small creeks and streams" and other areas.

"Six to 10 inches of rainfall has fallen over the last 24 hours. An additional four to six inches will be possible through the afternoon hours," the warning said.

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 had been 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 "LSU streets are impacted by water. Please stay away from campus if possible." and that 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.

CNN's Kevin Conlon contributed to this report