COLUMBUS, Ohio - Police shot and killed a man who stormed into a central Ohio restaurant wielding a machete and randomly attacking people as they sat unsuspectingly at their dinner tables, according to US media reports.

Four people were injured in the attack on Thursday evening (US timezone), in the city of Columbus.

The suspect was the only one killed, said CNN.

Nobody inside the Nazareth restaurant and deli said they knew him, CNN reported police as saying.

"(He) immediately began swinging a machete at customers and employees inside," Columbus police sergeant Rich Weiner said.

"There was no rhyme or reason as to who he was going after as soon as he walked in, according to some of the witnesses."

According to CBS News, investigators have identified the suspected attacker as Mohammad Barry.

It said investigators were running down leads to try to determine if the attack was somehow tied to terrorist organisations.

"Right now there's nothing that leads us to believe that this is anything but just a random attack," Weiner said.

CBS described the restaurant as Mediterranean, and said victims of the attack had been taken to an area hospital and were expected to recover.

One victim who was in critical condition underwent surgery and is now "stable," Weiner said.

Karen Bass was inside the restaurant when it all happened, CNN reported.

"He came through the front door and then started just systematically hitting people," she told CNN affiliate WSYX.

"I thought it was a personal thing, and then he just started down the row hitting everybody."

She told WBNS: "There were tables and chairs overturned, there was a man on the floor bleeding, there was blood on the floor.

"I fell like five times. My legs felt like jelly. I just thought he was going to come behind me and slash me up," she said, describing her frantic escape.

According to CNN, the suspect was seen 30 to 45 minutes earlier entering the restaurant and speaking with an employee. Police would not discuss details of that conversation.

He left, came back at around 6pm and then attacked a man and woman at a booth just inside the door, Weiner said.

Two men immediately ran out and called 911 while another engaged in a "physical altercation" with the suspect.

"Some of the patrons there started throwing chairs at him just trying to get him out of there," Weiner said.

The man eventually fled the scene in a white car and led police on a short chase.

Officers forced the man off the road a few miles away and when he got out of his car police said they tried unsuccessfully to use a stun gun on him.

Weiner said, "At that point he had a machete and another knife in his hand and he lunged across the hood at the officers."

That's when police said an officer shot and killed the man.

The Federal Bureau of Investigation is helping local police with the investigation, which includes trying to determine the attacker's motive.