Eyewitnesses in a nearby residential area said the Boeing-737-500 caught fire while airborne, at around 5:15 a.m. local time (23:15 GMT Saturday).
The plane, owned by Russian flagship air carrier Aeroflot, was carrying 82 passengers and six crew members, the airline and the emergencies ministry said.
Aeroflot said the passengers on Flight 821 included seven children, and "foreign citizens including nine from Azerbaijan, five from Ukraine, and one from each of France, Switzerland, Latvia, the United States, Germany, Turkey and Italy."
Russian TV channels have shown footage of a section of the Trans-Siberian rail line strewn with charred pieces of the plane's wreckage.
An eyewitness told Vesti-24 that she had been woken by an explosion, and that neighbors had seen the burning plane hurtling downwards "like a comet."
Russia's president and prime minister have sent messages of condolence to the families of those killed, the Kremlin and government said.
Prime Minister Vladimir Putin said in his message to the Perm Territory's governor: "I ask you to convey a word of support and deep sympathy to those who lost what is dearest to them - their relatives and close ones."
"A government commission will do all it can to investigate the circumstances of this catastrophe, and to provide help to the families of those who died," Putin's message, quoted by the government press service, said.
The Kremlin quoted a message from President Dmitry Medvedev to Perm Territory Governor Oleg Chirkunov, also expressing "sympathy and support" to the families.
The Perm Territory will hold a day of mourning for the crash victims on Monday, a spokesman for the regional administration told RIA Novosti.
CAUSE OF THE CRASH
Investigators have yet to ascertain the cause of the disaster, but a police source in Perm said the crash could have been caused by one of the plane's engines catching fire and failing.
Russian Transportation Minister Igor Levitin, who is heading the government commission investigating the catastrophe, told RIA Novosti that the plane's black boxes had been found and passed on to experts.
"The flight data recorders have been found, and handed over to the Interstate Aviation Committee [of 12 ex-Soviet states], which will decode it," he said.
The Perm Territory's emergencies ministry department has published a list of those killed in the crash, which includes Col. Gen. Gennady Troshev, 61, a former commander of the North Caucasus Military District.
The youngest of those on the passenger list is a nine-year-old girl, Yana Kuznetsova.
Chechen President Ramzan Kadyrov said a street in Grozny would be renamed in honor of Troshev, who commanded federal forces during the 1994-1996 First Chechen War, and became the top commander in the North Caucasus in 2000. He was dismissed two years later by then-president Vladimir Putin.
Moscow's Sheremetevo Airport announced that a plane carrying 18 relatives of some of those killed had left Moscow for Perm.
An airport spokesman told RIA Novosti that the relatives had been put on a scheduled Aeroflot flight, and that if other relatives wish to travel to Perm, a reserve aircraft is available to take them there without charge.
The emergencies ministry said three people who had tickets for Flight 821 had failed to register on time for flight 821 at Sheremetevo on Saturday evening, and did not board the plane.
AEROFLOT BREAKS WITH SUBSIDIARY
Aeroflot announced on Sunday it has severed ties with its subsidiary that owned the plane.
"A decision has been taken to completely sever cooperation with our subsidiary Aeroflot-Nord. All future flights will be carried out by our companies separately," Aeroflot Director Valery Okulov told reporters at Sheremetevo Airport in Moscow.
Okulov said the subsidiary will no longer be allowed to use the Aeroflot brand for its operations.
He said the company had paid "too great a price" for its ties with Aeroflot-Nord.
Aeroflot pledged in a statement to pay bereaved families up to 2 million rubles ($80,000) in compensation per victim.
RAIL TRACK REPAIRED
The plane crash damaged a 50-meter (160-foot) section of railtrack linking Yekaterinburg to Perm.
A spokesman for Russian Railways told RIA Novosti that the east-bound part of the track has been fully repaired, and journeys have resumed.
Perm is located around 1,200 kilometers (750 miles) east of Moscow.
The disaster is Russia's worst since Pulkovo Flight 612, which crashed in eastern Ukraine on August 22, 2006 en route from the Russian Black Sea resort of Anapa to St. Petersburg, killing all 160 passengers and 10 crew.
The Boeing 737-500 was launched in 1987, and entered service in 1990. The plane is highly popular among Russian airlines, which often buy second-hand models to replace Soviet-built airliners.
The Boeing 737 is the most-used and most-produced passenger jet in the world. The earliest variants of the jetliner entered service in 1968.
The most recent accident in the post Soviet space involving a Boeing 737 was on August 24, when a Boeing 737-200 crashed in Kyrgyzstan in Central Asia, killing at least 65 people.