ROCHESTER — A tour bus likely had a front tire blowout just before it veered off a highway and overturned, killing two passengers and injuring 35 people, three seriously, state police and a company spokesman said Monday.

The driver of the Niagara Falls-bound bus, which was carrying Indian nationals from Washington, D.C., lost control Sunday and ran off Interstate 390 into woods near Avoca, 55 miles south of Rochester.

Ambulances and helicopters took seven of the most seriously injured victims to a hospital in Rochester, and three were in guarded condition there Monday. State police said they are expected to survive.

The bus, owned by Bedore Tours of Wheatfield, left Washington on Sunday morning on a leg of the group’s tour of the United States and stopped for lunch in Pennsylvania, State Police spokesman Mark O’Donnell said.

Dan Ronan of the American Bus Association, speaking for its member Bedore, said the driver called company-owner John O’Hare from his hospital bed after the wreck.

“The driver does not know what happened,” Ronan said. “He was going along and the tire blew and he lost control.”

The front tires on the bus were new, having been replaced within the past couple of months, and the bus was a 2007 model, he said.

Ronan said a federal inspection completed in February 2010 gave the 61-year-old firm a “satisfactory” rating, the top of three grades. He said the review found 12 vehicles inspected from the fleet of 19 were in good working order, but it wasn’t clear if the bus in the accident was inspected.

Two messages posted on Bedore Tours’ Facebook page late Monday afternoon extended sympathies to the families.

“Bedore Tours is deeply saddened about Sunday's accident which claimed the lives of two of our passengers and injured numerous other tourists and our driver. Bedore Tours takes its responsibility very seriously to get our passengers to and from their destination safely,” reads the first message posted. “We are doing all we can to assist the families of the victims and we are cooperating fully with all of the law enforcement agencies to find the cause of this accident. In these difficult times, Bedore Tours extends its deepest sympathies to the families of the passengers who perished and those who were injured.”

The bus driver, 58-year-old John Dinardo Jr., had no history of driving violations or criminal activity and his logbook was in order, New York State Police Superintendent Joseph D’Amico said.

“There is no evidence of any excess speed, of any alcohol, of any driver fatigue or of any other violation,” D’Amico said. “We believe it was just a blowout of the right front tire, but the investigation is continuing.”

Based on markings in the road and witness statements, “everything appeared to be normal, traveling along,” D’Amico said. “They heard this loud bang, which we’re assuming was the blowout on the front tire.”

The bus veered on the roadway and then ended up on the embankment, where it flipped over to the driver’s side, slid into a wooded area and came to a stop.

Investigators planned to interview Dinardo and witnesses and to inspect the vehicle to determine if there were any mechanical problems, O’Donnell said.

One of the dead was identified as Sakina Kiazar, 52, of New Delhi. The name of the other, a 66-year-old woman, was withheld pending notification of relatives. Twenty passengers remain hospitalized Monday.

Only the driver’s seat had a safety belt, and the driver was wearing it at the time of the crash, D’Amico said. Tour buses are not required to have belts for passengers.

D’Amico said the tire’s manufacturer will work with state police to examine the tire and that a data recorder aboard the bus will be examined to gauge things such as speed, tire pressure, engine temperature and other factors.

So far this year, 32 people have been killed and 323 injured in 17 tour bus accidents, according to Advocates for Highway and Auto Safety. That’s more than in all of 2010, when there were 30 killed and 272 injured in 28 crashes.

Tour bus industry safety has drawn heightened attention since the March 12 crash of a bus returning to New York City’s Chinatown after an overnight excursion to a Connecticut casino. Fifteen people were killed when the bus flipped onto its side and struck a pole, peeling off its roof.

A passenger has said the driver fell asleep; the driver has said he was alert and well-rested. That crash is being investigated by state police and the National Transportation Safety Board.

State Transportation Commissioner Joan McDonald said there have been about 3,000 surprise bus inspections throughout the state since the March crash. During that period, 304 drivers and 238 buses have been taken off the road. The state does 160,000 bus inspections every year.

In January 2005, a bus chartered by a Canadian women’s youth hockey team rammed a parked tractor-trailer along I-390 near Geneseo, about 30 miles north of Sunday’s crash, killing four people. Investigators determined the driver’s lack of sleep and inexperience led to the crash.