Several massive tornadoes churned above Oklahoma on Monday, killing at least two people, with hail as big as grapefruit hitting the US state, the authorities and US media said.

The storms began forming in southern parts of the state in the afternoon, local media reported, with the first confirmed twister hitting near Elmore City, in rural Garvin County.

"Strong winds and hail as large as grapefruits were reported," a News9 television broadcast said. "It was nearly a mile wide."

Roofs were ripped off homes, and an empty bus was blasted upward and left dangling in a tree, the channel reported.

A second confirmed tornado then ripped across the southwestern town of Ninnekah, just an hour after the first.

Videos posted on social media showed large, dark cloud funnels moving quickly across the landscape.

A 76-year-old man was killed when a tornado hit his home, CBS news reported Garvin County Sheriff Larry Rhodes as saying.

Another man was reported killed in the nearby town of Connerville.

Aerial video taken along the storm paths by local media showed houses ripped apart by the tornadoes, as well as trees uprooted and mobile homes toppled.

Another storm later produced a third tornado and there were reports of smaller twisters along with golf ball-sized hail that damaged houses and other buildings.

Local television stations reported many people were unaccounted for.

A tornado also touched down in central Iowa, the National Weather Service reported, saying there were no immediate reports of damage. Another twister hit near the state of Nebraska, it said.

The storms are expected to move into the Ohio and Tennessee valleys on Tuesday, forecasters said.

Another storm system may sweep across northern Texas to Missouri on Wednesday.

The National Weather Service has issued a tornado watch for parts of Arkansas, Louisiana, Missouri and Texas.