State police said the bus was on a return trip from Las Vegas, Nevada, to Vancouver. The bus careened through a guardrail along the icy Interstate 84 and fell down a steep embankment.
RCMP in British Columbia say they've been asked to help notify the relatives of people on the tour bus.
Sgt. Peter Thiessen will only say the Mounties have been asked to contact next of kin in B.C.'s lower mainland and beyond.
"Oregon state police has requested our assistance in regards to that tragic crash in their jurisdiction and requested that we assist in some of the next of kin notifications that may need to be done here in the lower mainland or even outside the lower mainland," said Thiessen in an interview.
"So as we do them, those notifications, we will be supporting those families that are affected and will be providing information back to the Oregon State Police in regards to those next of kin notifications."
But he declined to answer questions regarding the nationalities of the people involved. State police have said that they are having difficulties getting witness accounts of the crash due to a language barrier.
St. Anthony Hospital in Pendleton treated 26 people from the accident, said hospital spokesman Larry Blanc. Five of those treated at St. Anthony were transported to other facilities.
The cause of the crash is not known. The bus driver survived the crash but has not been able to communicate with investigators because of the severity of the driver's injuries.
Police say the bus, carrying 40 passengers, lost control around 10:30 a.m. PT on the snow- and ice-covered lanes of Interstate 84 in eastern Oregon. The bus crashed through a guardrail and went down an embankment dozens of metres.
Lt. Greg Hastings said the accident happened in the west end of Blue Mountains, on an 11-kilometre section of road that winds down a hill west of an area called Deadman Pass.
Rescue workers used ropes to help retrieve people from the crash scene.
According to CBC News' Lisa Johnson, the bus company is owned by the B.C.-based Mi Joo Tour and Travel, which has offices in Vancouver and Coquitlam.
NBC's Jane Sander, who was on the scene, told CBC News that the bus was on its side and in terrible condition.
"The bus is mangled with the roof ripped off the back part of the bus, and the front is smashed in," she said.
"Some of the wheels are ripped off the sides."
A bus safety website run by the U.S. Department of Transportation said Mi Joo Tour & Travel has six buses, none of which have been involved in any accidents in at least the past two years.
A spokesman for the American Bus Association, Dan Ronan, said buses carry more than 700 million passengers a year in the U.S.
"The industry as a whole is a very safe industry," said Ronan. "There are only a handful of accidents every year. Comparatively speaking, we're the safest form of surface transportation."
The bus crash was the second fatal accident in Oregon on Sunday morning due to icy conditions. A 69-year-old man died in a rollover accident.