OKLAHOMA CITY — Waterlogged parts of the central U.S. braced Wednesday for more rain, following days of severe storms that have battered Iowa, Kansas, Missouri and Oklahoma and caused at least three deaths.

Authorities urged residents of several small towns in Oklahoma and Kansas to leave their homes as rivers and streams rose. In the Missouri capital of Jefferson City, the mayor issued a mandatory evacuation for an area involving a handful of homes. The city’s airport also has been evacuated.

The Arkansas River was approaching historic highs, while the already high Missouri and Mississippi Rivers were again rising after a multi-day stretch of storms that produced dozens of tornadoes. Forecasters predicted parts of Oklahoma, Missouri and Kansas could see more severe weather Wednesday night into Thursday.

“The biggest concern is more rain,” Oklahoma Gov. Kevin Stitt said during a news conference following an aerial tour with Tulsa Mayor G.W. Bynum and other officials Wednesday morning.

The deluge inundated roadways, closing highways in 22 Oklahoma counties and 17 Kansas counties, along with more than 330 Missouri roads. Amtrak suspended train service Wednesday and Thursday along a route between St. Louis and Kansas City because of congestion and flood-related delays.

The Arkansas River, which was just above 37 feet (11 meters), or 9 feet (2.74 meters) above flood stage, at Muskogee, Oklahoma, was expected to eventually reach 43.5 feet (13.26 meters). Officials encouraged residents in several communities along the river to leave their homes.

But Bynum, Tulsa’s mayor, said his city of more than 400,000 people was safe so far.

“The levee system is working the way it’s supposed to right now,” he said.

Near Crescent, about 34 miles (55 kilometers) north of Oklahoma City, erosion left several homes hanging over the swollen Cimarron River. One unoccupied home rolled into the river Tuesday, and authorities say others could collapse.

More than 9 inches (23 centimeters) of rain has fallen since Sunday in parts of Oklahoma after an already rainy spring.

“Any rainfall we get just continues to saturate the soils that are already saturated. Especially rivers and streams,” said Oklahoma State Climatologist Gary McManus.