Kentucky Governor Andy Beshear said hundreds of people stranded by flooding had to be rescued.
President Donald Trump approved the state's request for a disaster declaration, authorising the Federal Emergency Management Agency to co-ordinate relief efforts throughout the state.
Beshear said most of the deaths, including a mother and seven-year-old child, were caused by cars getting stuck in high water.
"So folks, stay off the roads right now and stay alive," he said on Sunday.
"This is the search and rescue phase, and I am very proud of all the Kentuckians that are out there responding, putting their lives on the line."
Beshear said 1000 rescues has been carried out across the state since the storms began on Saturday.
The storms knocked out power to about 39,000 homes, but Beshear warned that harsh winds in some areas could increase outages.
Parts of Kentucky and Tennessee received up to 15 centimetres of rain, said Bob Oravec, a senior forecaster with the National Weather Service.
"The effects will continue for a while, a lot of swollen streams and a lot of flooding going on," he said.
In Alabama, the weather service in Birmingham said it had confirmed an EF-1 tornado touched down overnight in Hale County.
Storms there and elsewhere in the state destroyed or damaged a handful of mobile homes, downed trees and toppled power lines, but no injuries were immediately reported.
A state of emergency was declared for parts of Obion County, Tennessee, after a levee failed on Saturday, flooding the small community of Rives, home to about 300 people in the western part of the state.
In Atlanta, a person was killed when a large tree fell on a home early Sunday, according to Atlanta Fire Rescue Captain Scott Powell.
Dangerously cold wind chill temperatures as low as 50C were expected in most of North Dakota, which remained under an "extreme cold warning" along with large swathes of South Dakota and Minnesota.
Water submerged cars and buildings in Kentucky and mudslides blocked roads in Virginia late Saturday into Sunday.
Both states were under flood warnings, along with Tennessee and Arkansas.
Ice and snow made road travel treacherous in large swathes of Michigan, which remains under a winter weather advisory until Monday afternoon, while authorities in Colorado reported eight people had been killed in fatal vehicle crashes since Valentine's Day.
Meteorologists said the US was about to get its 10th and coldest polar vortex-stretching event this season, with the northern Rockies and northern plains first in line.
Weather forces in the Arctic are combining to push the chilly air that usually stays near the North Pole into the US and Europe.
