The police pursuit began at approximately 10 p.m. local time Friday, (11 p.m. E.T.,) on Interstate 94 in Wisconsin, a spokesperson for Greyhound said. The bus was travelling from Milwaukee to Chicago.
Eventually, the bus stopped and the passengers were escorted off the Greyhound one by one, Williams said.
The chase late Friday started in southern Wisconsin and ended in northern IL.
Police say all 36 passengers were removed from the bus and the suspect was taken into custody without incident.
The Racine County sheriff said on Saturday that Vargas-Rosas is an illegal immigrant who has been deported before.
Vargas-Rosas is being held at the Lake County Jail in Waukegan. The caller stated a man on the bus was threatening to shoot people.
"The suspect was ordered out at gunpoint", the sheriff said.
Authorities are saying that a verbal altercation between passengers turned into threats on a Greyhound bus Friday night. No injuries were reported, according to WGN.
But the sheriff's office is going to continue to search it and piece together stories from the witnesses on board.
"I think he ultimately recognized that this was a serious event when we spiked his tires", Schmaling said of the driver. Authorities are looking to extradite him back to Wisconsin, where he is facing charges of making terroristic threats.