Hurricane Barry pushed ashore along the Louisiana coast west of New Orleans on Saturday and quickly weakened to a tropical storm. But its torrential downpours still promise the risk of "life-threatening" inland floods in Louisiana and Mississippi, the National Weather Service said.

The storm moved farther inland across the north-central Gulf Coast Saturday evening and forecasters warned of flooding across the Lower Mississippi Valley, the National Hurricane Center (NHC) said.

Louisiana Gov. John Bel Edwards said Barry may be losing steam, but it still packs a punch.

"Don't let your guard down," he said in a news conference late Saturday night. "My concern is people are going to bed thinking the worst is behind us and that may not be the case."

Edwards said President Donald Trump called him Saturday to offer his help.

Edwards said the Coast Guard rescued at least 11 people early Saturday morning who were trapped in southern Terrebonne Parish. He expects more search-and-rescue operations will be needed.

He emphasized no Mississippi River levees have been topped or breached, saying there had been some confusion because of photos and videos of water going over "back levees" in Plaquemines Parish.

He said the storm will slowly move north, blanketing most of the state with rain.

"It's going to be a long few days, and there are going to be some significant challenges," Edwards said.

Barry packed sufficiently powerful sustained winds – 75 mph – to qualify as the nation's first hurricane this season when it hit shore Saturday near Intracoastal City, Louisiana, about 150 miles west of New Orleans.

Moving inland, Barry dropped to sustained winds of 50 mph and was centered 35 miles southwest of Alexandria, Louisiana, as of 11 p.m. EDT, according to the NHC. It was moving north-northwest at about 8 mph.

The center of the storm was forecast to move across central Louisiana Saturday, through northern Louisiana on Sunday, and over Arkansas Sunday night and Monday.

A hurricane warning for the Louisiana coast was dropped to a tropical storm warning, but officials warned that heavy rains pose a risk of flooding. A storm surge warning – a risk of flooding from rising waters moving inland from the coastline – was in effect from Intracoastal City to Biloxi, Mississippi, and Lake Pontchartrain.

Forecasters said Barry could unload 10 to 20 inches of rain through Sunday across a swath of Louisiana that includes New Orleans and Baton Rouge, as well as southwestern Mississippi, with pockets in Louisiana possibly getting 25 inches.

Watch Live:Webcams show Barry's landfall in New Orleans and the Louisiana coast

That is a lot of rain:How will Barry compare to Louisiana's 2016 flooding?

NHC Director Ken Graham warned slow-moving rain cells would create especially dangerous flooding conditions in southeastern Louisiana, as well as Arkansas, Missouri, Mississippi and parts of Tennessee into next week.

"When you put that much rain down in areas around Baton Rouge and Mississippi, those rivers and creeks are filling quickly," he said.

“That is just an amazing amount of moisture,” he said on Facebook Live, pointing to a weather data board. “That is off the chart.”

Even with winds below hurricane strength, the storm still puts locals at risk. Graham stressed that in the past three years, inland flooding has accounted for 83% of the deaths during tropical cyclones, half of those in vehicles.

He warned conditions could become especially dangerous at night with heavy rains that could make driving difficult.

"It's really best not to be on the roads, especially if it's flooding," Graham said. "Turn around and don't drown."

The hurricane brings a tornado threat, too. The highest-risk area is on the east side of the storm, along the Mississippi coast, and Mobile Bay, Graham said.

As the storm drew closer Saturday morning, the Coast Guard said it was rescuing about a dozen people stranded by flooding on a remote Louisiana island that has been shrinking for years.

Petty Officer Lexie Preston told the Associated Press some of the people were on rooftops on Isle de Jean Charles, about 45 miles south of New Orleans. He said four people and a cat had been removed by helicopter and a boat was heading to the area to help get the rest of the people off the island.

What about dogs? Rescue dogs flown out of Louisiana ahead of Barry to avoid euthanasia. They're adoptable

Anthony Verdun chose to ride it out in his home in Isle de Jean Charles, despite watching the water rise 8 feet in 10 minutes near his raised house.

Verdun, noting his refrigerator was still stocked with a fresh catch of fish from Friday, said he waved off a Coast Guard helicopter Saturday morning that hovered above his house, one of the highest on the island.

"I gave them the all good," Verdun said via text message. "My son is in the (Coast Guard) and he told me how to signal so we signaled back, 'All clear.' "

Early Saturday, water spilled over a "back levee" in Plaquemines Parish, outside New Orleans. This sort of spillage is not uncommon after heavy rain, officials said.

Gov. Edwards assured residents the levees were "stronger than they've ever been" and the state was better prepared than ever.

The threat to New Orleans diminished late Friday. Officials said the levee system would crest Monday at only 17 feet at the critical Carrollton gauge. That is about 3 feet lower than a previous forecast and 2 feet below the levee's height.

For the first time since Hurricane Katrina ravaged the city 14 years ago, the governor said all floodgates were sealed in the Hurricane Risk Reduction System. The city did not offer any sandbags, although some businesses did make them available.

Residents of the Big Easy had been urged to “shelter in place” in lieu of evacuation orders, which are normally issued only for Category 3 hurricanes.

More than 100,000 people were without power as the storm hit Louisiana Saturday.

The World Central Kitchen, a nonprofit that provides meals during natural disasters, was working with local volunteers to provide hot meals to evacuees and first responders.

Until the rain falls in force, the number of hungry folks will remain up in the air.

Contributing: Doyle Rice, Olivia Sanchez, USA TODAY; Andrew J. Yawn, Leigh Guidry, Nick Siano, Lafayette Daily Advertiser; Greg Hilburn, Monroe News-Star; Associated Press