"All the bodies have been found and fragments of bodies have been collected," Interfax news agency reported, quoting an unnamed source in the investigation team.
About 20 of the bodies were likely to be difficult to identify because of the poor state of the remains, the source said.
Meanwhile, Russian federal aviation service head Alexander Neradko said that the two black box flight recorders recovered from the plane would be sent to Moscow to be decoded, RIA Novosti reported.
Russian Transport Minister Igor Levitin, who is overseeing search efforts said that officials were examining recordings of conversations between the pilots and a Ukrainian air traffic control post in Kharkiv.
The plane, a Tupolev-154 jet, was on a flight from the Russian Black Sea coast city of Anapa to Saint Petersburg when it ran into severe weather and crashed on Tuesday, officials said.
Many relatives of the 170 victims, who included 45 children under 12, arrived at Donetsk in preparation for the flight to the scene of the crash 45 kilometres to the town’s north.
Criminal inquiry opened
At the crash site, Russian prosecutors, who have opened a criminal inquiry into possible safety violations, photographed the victims' remains.
Orthodox priests held a memorial service near the wreckage, which was scattered over a wide swampy area, where plane parts and the land lay scorched.
An AFP reporter saw around 50 black plastic body bags placed onto stretchers by emergency workers and lined up along the ground near the crash site.
Ukrainian President Viktor Yushchenko and Russia's President Vladimir Putin have declared national days of mourning in Ukraine and in Russia.
A spokesman for jet owners Pulkovo airlines said that the crash victims included five Western nationals from Finland, France, Germany and The Netherlands.
Officials blamed the crash on stormy weather in the area on Tuesday, with a spokeswoman for Russia’s emergency ministry quoted as saying the crash occurred as the result of a lightning strike.
Ukrainian officials said the plane was flying at 10,000 metres when the crew declared an onboard fire and began to prepare for an emergency landing.