LIVINGSTON, La. — With thousands of people forced to flee their homes as floodwaters saturated the southern part of the state, the leader of the Federal Emergency Management Agency said Tuesday that Louisiana was confronting “a very large disaster.’’

“We know this has been a significant impact here in Louisiana,’’ W. Craig Fugate, the FEMA administrator, said at a news conference in Baton Rouge, the state capital, where officials said that more parishes were being added to a federal disaster declaration.

Governor John Bel Edwards said that although more than 20,000 people had been rescued statewide, Louisiana officials had confirmed 10 deaths. The state, the governor acknowledged, does not know how many people are missing.

Nearly 8,100 people slept in shelters Monday night, said Edwards, who added that about 40,000 homes had been “impacted to varying degrees.’’

“We are still very much in an emergency, search-and-rescue response mode for much of the Florida parishes,’’ Edwards said, referring to an eight-parish area east of the Mississippi River. “Saving life is the most important priority that we have. We’re going to dedicate every available response to that effort until it’s no longer required.’’

Although Louisiana faced substantial flooding in March, government officials and weather experts alike described this episode as far more severe. In Livingston Parish, a weather monitoring station recorded more than 25 inches of rain in three days.

“This is an unprecedented event here,’’ said Barry D. Keim, the state climatologist. “There is nothing in the recent past that even comes close.’’

Keim and other forecasters said they had begun tracking the storm system in early August and watched as it moved to the northwest. But the scale of the storm left many people here reeling.

“When a tropical wave is coming at you, that doesn’t really instill a lot of fear, and the Weather Service knew a heavy rainfall event was likely to happen,’’ Keim said. “But I don’t think anybody knew just how bad it was going to be.’’

Tens of thousands of people were without electricity Tuesday, and Edwards said restoring service was a priority. He also urged residents to register for federal disaster assistance.

“I want everybody out there to understand: Nobody has been forgotten,’’ Edwards said. “This is a very difficult situation.’’

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