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Vladimir Putin admitted Saturday Russian air defence was working when an Azerbaijani Airlines plane tried to land in Grozny before crashing, while stopping short of claiming responsibility.
The Kremlin said Putin apologised to Azerbaijani leader Ilham Aliyev over the "tragic incident" in a phone call, but did not say Russian air defence shot the plane.
Moscow had hitherto said that Grozny, where the plane was due to land but instead crashed in western Kazakhstan, was attacked by Ukrainian drones that day.
Baku, meanwhile, said Aliyev had "emphasised" to Putin the plan was hit by outside interference over Russia.
And on the streets of Baku, several residents AFP spoke to said they expected an official apology from their Russian ally.
Moscow said Putin had told Aliyev the plane had tried to land in Grozny "several times".
"During this time, Grozny, (the town of) Mozdok and Vladikavkaz were being attacked by Ukrainian combat drones and Russian air defence was repelling these attacks," Putin said, according to a Kremlin transcript.
It added that: "Vladimir Putin had presented his apologies that the tragic incident happened in Russia's air space and again expressed his deep and genuine condolences to the families of the dead, wishing a quick recovery to those affected."
A statement from Aliyev's office on the phone call appeared to show no doubt that the plane was hit over Russia.
"President Ilham Aliyev emphasised that the Azerbaijan Airlines passenger plane encountered external physical and technical interference while in Russian airspace, resulting in a complete loss of control," Baku's presidency said.
It added Aliyev "highlighted that the multiple holes in the aircraft's fuselage, injuries sustained by passengers and crew due to foreign particles penetrating the cabin mid-flight, and testimonies from surviving flight attendants and passengers confirm evidence of external physical and technical interference."
Survivors have told the media about hearing an "explosion" as the plane attempted to land.
Aliyev's office said Baku wanted an investigation "ensuring those responsible are held accountable."
Putin also called his Kazakh counterpart Kassym-Jomart Tokayev and said Moscow was committed to taking part in an "objective and transparent" investigation into the crash.
Speculation has swirled for days that Russia accidentally shot down the plane, with the US weighing in Friday saying it had "early indications" the plane was shot.
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Ukraine's Volodymyr Zelensky said he also spoke to Aliyev Saturday and called on "every country to put pressure on Russia to stop the lies about this disaster."
He accused Moscow of the "same lies that were told about MH-17" -- the Malaysian Airlines plane, which international investigations have said was downed by a missile shot by Russian-backed rebels in east Ukraine in 2014.
The EU's top diplomat Kaja Kallas said the crash was a "stark reminder" of MH17 and called for a "swift, independent international investigation."
A series of airlines have this week been cancelling flights to Russia after the incident, including flydubai and Israel's El Al.
The vast majority of Western airlines have stopped flights to Russia since Moscow launched its Ukraine offensive.
While Kazakhstan -- a key Russian ally -- has had a muted reaction to the crash and not blamed Moscow, some officials in Azerbaijan, which also has close ties to the Kremlin, called for an apology.
On Friday, Azerbaijani lawmaker Rasim Musabekov urged Russia to "accept this, punish those to blame, promise that such a thing will not happen again."
This feeling was reflected on the streets of Baku Saturday, where the mood was sombre.
"Just look at the damage, how many people's homes were filled with mourning just before the New Year," said 64-year-old teacher Rafiga Mammadova.
Others called for a public apology.
"We could have had such an incident as well," 41-year-old Teymur Mammadov said, in a country used to decades of conflict with neighbouring Armenia.
"Such things happen. However, they should apologise."
Officials from Kyrgyzstan, meanwhile, visited three survivors of the crash in the city of Aktau where the plane crashed in Kazakhstan, releasing footage of men in hospital beds whom they said will be transported home soon.
Several survivors and several bodies from the crash were brought to Baku late on Friday.