Flight 821, operated by an Aeroflot subsidiary, carried 82 passengers, including six children under 10, and six crew members, Aeroflot said.
Aeroflot officials said the plane was circling at about 3,600 feet in "difficult weather conditions" - including low cloud cover and rain - when it lost contact with ground dispatchers.
Witnesses said the plane was on fire as it fell.
"I felt an explosion, it threw me off the bed," a woman in Perm who was not identified told Vesti-24 television. "My neighbors, other witnesses told me that it was burning in the air, it looked like a comet. It hit the ground opposite the next house, trailing like fireworks in the sky."
It crashed around 3:15 a.m. on the outskirts of Perm, about 750 miles east of Moscow.
The most likely cause was engine failure, Vladimir Markin, a spokesman for the federal prosecutors' Investigative Committee, said in televised comments.
The head of the Investigative Committee said examination of the site showed the crash "apparently was connected to technical failure and a fire in the right engine," the ITAR-Tass news agency reported.
"There is much evidence for this," Alexander Bastrykin was quoted as saying.
The plane's flight recorders have been found, and officials said it will take three to four weeks to analyze them.
The passenger jet fell on a railroad embankment, damaging a section of the track. Parts of the plane's fuselage reading "Aeroflot" and "Boeing" lay askew on the rails, along with clothing, life preservers and engine parts.
Emergency workers in camouflage uniforms picked up human remains and placed them in blue bags. Relatives of passengers said they were asked to provide DNA samples to help in the identification. Part of the Trans-Siberian railway was shut down temporarily as a result of the rail damage, but traffic was restored later in the day, the national railroad company said.
Pavel Shevchenko, a 36-year-old Perm resident who lives just 300 yards from the crash site, said he was awoken by an explosion and ran outside. He said a neighbor who saw the crash told him the plane hit the ground at a 30- or 40-degree angle. Shevchenko said he feared his acquaintances or friends could be among the dead.
"It's awful. There's just no words to describe it. Perm is a small town, everybody knows everybody else here," he told The Associated Press. Perm is an industrial center with a population of about 1 million.
There was also some relief that the plane had not hit any homes when it crashed.
"I think the pilots did everything to save the city," Tatyana Sokolova, a Perm resident, said through tears on Vesti-24 television.
Russia and the other former Soviet republics have some of the world's worst air traffic safety records, according to the International Air Transport Association. Experts blame weak government regulation, poor pilot training and a cost-cutting mentality among many carriers.
No problems were reported with the 15-year-old jet when it was last inspected at the beginning of 2008, Aeroflot deputy director Lev Koshlyakov said.
Among those killed was Gennady Troshev, 61, an army general who commanded troops in Chechnya. Human rights activists had accused him of tolerating rampant abuses in the war-ravaged republic.
Troshev, who was dismissed in 2002 during a power struggle within Russia's armed forces, was traveling to Perm to attend a wrestling competition, news agencies said.
Citizens of Azerbaijan, France, Germany, Italy, Latvia, Switzerland, Turkey, Ukraine, and the U.S were among those killed, the airline said. The U.S. Embassy said the man listed as an American is not a U.S. citizen and no Americans appeared to have been on the flight.
Sunday's crash was the second involving a Boeing 737 in the former Soviet Union in the past month. A Boeing flying from the Central Asian nation of Kyrgyzstan to Iran crashed shortly after takeoff Aug. 24, killing 64 of the 90 people on board.
The pilot of that plane has been detained by prosecutors, officials said this week.
Associated Press writers Dmitry Lovetsky in Perm, Russia; and Mike Eckel, David Nowak and Mansur Mirovalev in Moscow contributed to this report.