The blast early on December 31 damaged 48 apartments in a 10-storey building in the industrial city of Magnitogorsk, some 1700km east of Moscow.
The death toll has progressively risen in the past few days as rescuers battle blisteringly cold temperatures to recover people trapped under the rubble.
As of Thursday morning (local time), the bodies of 22 of the 37 dead had been identified, agencies cited the local branch of the emergencies ministries as saying.
Russia's Investigative Committee, which probes major crimes, has said it is still investigating the exact cause of the blast.
It said no traces of explosives had been found at the site. Initial reports attributed the blast to a gas explosion.
Gas explosions are relatively common in Russia because of ageing infrastructure and poor safety regulations surrounding gas use.
