Devastating floods in the southern US state of Tennessee have left at least 21 people dead and dozens missing, local officials said Sunday in what they warned was a preliminary toll.

Tennessee was hit Saturday by what meteorologists called historic storms and flooding, dumping 15 inches (38 centimetres) or more of rain.

Rural roads, state highways and bridges were washed out and widespread power outages affected thousands of people.

Twenty people died in the town of Waverly, in Humphreys County, Police Chief Grant Gillespie said in a news conference covered by NewsChannel 5 Nashville.

Humphreys County is about a 90-minute drive west of Nashville, the country music centre.

Gillespie told reporters that the other death was in a rural area elsewhere in the county.

Initially, some 40 people were reported missing, but by late afternoon that number had been cut in half. "We're hopeful that we're getting to the end of that list," Gillespie said.

Local officials in Waverly likened the unusually intense storm to a hurricane or a tornado and said water rose so quickly that some people were unable to escape.

Search and rescue operations were continuing Sunday, with workers going from home to home to search for victims or those needing assistance.

The Waverly Department of Public Safety posted on its Facebook page a list of names of missing people, and asked for the public's help to find them.

"We have several reported by first names only along with several missing children," the post said, urging people to inform authorities when someone on the list was found and is safe.

Missing children

In Washington, President Joe Biden began an afternoon press conference by expressing his "deepest condolences for the sudden and tragic loss of life" in Tennessee.

"I've asked the FEMA (Federal Emergency Management Agency) administrator to speak to Governor (Bill) Lee of Tennessee right away" and offer any assistance needed, Biden said.

Humphreys County Sheriff Chris Davis told a CNN affiliate that the dead included two toddlers. Davis himself lost a friend to the floods.

"They just went and got one of my best friends and recovered him. He drowned in this," the sheriff said. "It's tough, but we're going to move forward."

Half a dozen children were among the missing, Davis said.

Authorities imposed a nighttime curfew as efforts to account for the missing continued.

Photos posted on social media showed a row of homes nearly submerged in brown floodwater, cars flipped over or piled on top of one another, and roads covered in mud and debris. One picture showed a lone person sitting on a rooftop, awaiting rescue.

"The news media has been very focused on what's happening in other areas – Haiti, Afghanistan, hurricanes coming into the northeast – but I think that we need to understand that the devastation here in Tennessee has been every bit as significant," said US Senator Bill Hagerty after visiting a flood-devastated school.

The Piney River in nearby Hickman County crested nearly 12 feet (3.6 meters) above its historic record high, a local National Weather Service office said.