The plane was flying in a relief group of Russian miners and their families who work in the Norwegian coal mining settlement there.
The crash, the worst in Norwegian aviation history, happened as the chartered Tupolev jet approached the island's only airport.
The island governor's office said no survivors had been found and denied a claim from Moscow that five people had escaped from the wreckage.
"This is totally unknown to us and wrong," the Norwegians said.
"They must have walked away from the site without us noticing, so that has got to be wrong." A spokeswoman for the Russian Emergencies Ministry said they based their claim on a report from the crash site.
But a spokesman for Vnukovo Airlines, which had chartered the plane to the coal company that was flying the miners to the settlement, could not confirm this.
The accident occurred in bad weather six miles east of Longyearbyen.
Air traffic officials said they had lost contact with the aircraft shortly before it was due to land. The jet crashed at a remote site, with no roads nearby.
"No survivors have been found and our first aid staff are returning from the crash site," a local government official said.
The Norwegian aviation inspectorate said the plane was making a normal instrument landing .
The miners were travelling to work in one of the island's three open- cast coal mines. Some of them were accompanied by their families. The first rescuers arrived shortly after 1pm and reported that most of the three-engine jet's wreckage was scattered around the top of the small Opera mountain while the rest was found further down the slopes.
The miners, most of them Ukrainians, represented a considerable part of the Russian community on Spitzbergen, which numbers around 2,000 people.
They were due to replace more than 100 other Russian miners who should have returned to Moscow on the doomed flight.
Their colleagues wept when they were told the plane had crashed a few minutes away from the landing site, Nor- wegian radio reported.
Spitzbergen is a Norwegian coal-mining settlement and Russia and Norway share the island's resources under a treaty dating back to the 1920s.