Flooding in Rock Valley, Iowa, has forced evacuations and rescues in the town, which has about 4,000 residents. Credit...Chris VB/UGC, via Reuters

Parts of the Upper Midwest remained under flood warnings on Sunday after days of heavy rain caused major flooding, leaving at least one person dead in South Dakota and forcing evacuations and water rescues across the region.

Flood warnings were in place for rivers in parts of Illinois, Iowa, Minnesota, Nebraska, South Dakota and Wisconsin. A flood warning means that flooding is imminent or already occurring.

In South Dakota, torrential rain fell across the central and eastern parts of the state for three days. One person died as a result of the severe weather, Gov. Kristi Noem said at a news conference on Sunday. She did not provide any details about the person or the circumstances of the death. Several rivers in the state broke water-level records, and the Big Sioux River was projected to set a record of 42.2 feet on Monday afternoon, Ms. Noem said.

Officials were calling for voluntary evacuations in Dakota Dunes, a community of about 4,000 people near the bank of the river, and were planning to close a stretch of Interstate 29 on Sunday evening so that they could build a levee across the highway, she added. “This is probably the first time we’ve seen this kind of rainfall come this quickly,” Governor Noem said.

In Iowa, rivers have crested several feet above levels reported during a 1993 flood that left 50 dead across the Midwest, according to that state’s governor, Kim Reynolds. By Sunday, she had declared a disaster for more than 20 counties, and at a news conference she described the projected damage as “staggering.”

On Saturday alone, emergency responders had conducted 250 water rescues, more than 1,000 people had been sheltered, and more than 1,900 properties had been damaged, with hundreds destroyed, Ms. Reynolds said on Sunday.

Some cities were without power, others were without drinkable water. Hospitals and nursing homes had been evacuated and many businesses were shuttered.

“The devastation is severe and it’s widespread,” she added. “It’s not over yet.”

Officials in Iowa noted that more rain was in the forecast, especially over the eastern part of the state.

“This is a very serious flood that we’re in right now and it is not going to cease,” said John Benson, the director of the Iowa Department of Homeland Security and Emergency Management.

Flooding in southern Minnesota left “entire communities under feet of water,” Gov. Tim Walz said in a news release on Saturday.

Mr. Walz declared a peacetime emergency, authorizing the National Guard to aid local emergency responders. The city of Waterville received approximately 14 to 18 inches of rain, he said.

The flooding in the Midwest has caused devastation in Rock Valley, Iowa, where the Rock River rose to a record level early Saturday. That led city officials to issue emergency evacuation orders for many of the city’s 4,000 residents. The city was without clean water because its wells had been contaminated by floodwaters, the local authorities said on social media.

Sioux City Fire Rescue, which helped to evacuate people from Rock Valley, said on social media that many people and animals stranded in floodwaters in the city had been rescued by emergency teams with boats.

In neighboring Nebraska, Gov. Jim Pillen said in a statement that he had authorized a military helicopter to help with search-and-rescue operations.

Volunteers stacking sandbags in Hawarden, Iowa, a town of about 2,000 where some residents were evacuated.Credit...Tim Hynds/Sioux City Journal, via Associated Press

About 15 miles southwest of Rock Valley, parts of Hawarden, Iowa, were also evacuated, city officials said on social media. Hawarden has a population of about 2,000.

In Sioux Falls, S.D., emergency services rescued nine people from floodwaters, Regan Smith, the city’s emergency manager, said at a news conference on Saturday.