At least three Oklahoma riverfront communities were urged to evacuate due to flooding. (Reuters)

Weather forecasters on Wednesday expected drenching rains to roll into the storm-ravaged US southern and central states, where thunderstorms and tornadoes killed at least three people and triggered widespread flooding.

More than 30 tornadoes struck a swath from Texas to Iowa since Monday, according to the National Weather Service, and residents in at least three Oklahoma riverfront communities were urged to evacuate due to flooding.

One person was killed and another was injured when a tornado struck the rural town of Adair, Iowa, about 50 miles (80 km)west of Des Moines, at about 1:30 a.m. local time, the weather service said.

While the weakening storm system moved into the Great Lakes region early Wednesday, another system was expected to brew Wednesday night into Thursday, said Brian Hurley, a forecaster with the service's Weather Prediction Center.

"The southern Plains can't catch a break," Hurley said. "That whole area is still under the gun."

Rainfall is predicted to be about 2 inches (5 cm) across eastern Kansas, Oklahoma, and into western Missouri, with localized spots getting up to 5 inches (13 cm), he said.

In Oklahoma, heavy rainfall prompted the Army Corps of Engineers to plan to increase the water flow at the Keystone Dam on the Arkansas River by nearly 30%, putting some low-lying communities at risk.

State emergency officials issued evacuation advisories for residents in parts of the Tulsa suburb of Sand Springs, Fort Gibson, about 50 miles (80 km) southeast of Tulsa, and Webbers Falls, 70 miles (113 km) southeast of Tulsa.

"At this point it is voluntary," Oklahoma Department of Emergency Management spokesman Jerry Lojka said by phone.

"The major concern is that all of those communities are right on the Arkansas River," said Lojka. "They're pretty close to flood stage as it is and if they increase the flow, they're afraid that it's going to go over its banks."

In Missouri, cresting rivers prompted Governor Mike Parson to declare a state of emergency on Tuesday.

Forecasters said the Missouri River was expected to crest on Thursday at more than 32 feet (9.75 meters) at the state capital, Jefferson City. Local media said that would be 2 feet (61 cm) higher than the city's levees.

Two people died in a traffic accident late Monday on a rain-slicked Missouri highway, police said. Another seven people were injured in Wheatland when a tornado struck the Lucas Oil Speedway.