Downing Street said Mr Cameron called the Russian president on Sunday morning, a day after the plane went down in a desert region of the Sinai peninsula while flying from the Red Sea resort of Sharm el-Sheikh to St Petersburg.
A spokesman said: “The Prime Minister said how sorry he was about this terrible tragedy and that Britain shared the pain and grief of the Russian people,” the spokesman said.
“The Prime Minister added that Britain stood ready to help if there was anything we could do to establish the reasons behind the crash.”
All 224 people on board the Kogalymavia Airbus A321 died. Experts have recovered the plane’s black box recorders but Egypt’s president Abdel Fattah al-Sisi said an investigation into the causes of the crash could take months.
Russia’s Emergency Ministry says satellite shots showed the debris of the plane on the are of 16 square kilometers.
At least 163 of the bodies have already been recovered from the wreckage and moved to hospitals and morgues in the Egyptian capital Cairo.
About 100 Russian investigators have joined the search for remaining bodies and evidence at the crash site.
A local Islamist militant group affiliated to the Islamic State (IS) group said in a statement it had brought down the plane “in response to Russian airstrikes that killed hundreds of Muslims on Syrian land”.
A video posted on a website linked to the group purported to show the airliner blowing up in mid-air, but the footage could not be independently verified.
Russian and Egyptian officials have rejected claims of terrorist involvement.
Plane ‘broke up in air’
On Sunday afternoon a Russian aviation official told reporters the plane “broke up in the air” – but said it was too early to draw conclusions.
Russia’s transport regulator has issued Kogalymavia with an inspection order to check all its Airbus A321 planes.
The airline – which also trades under the name Metrojet – said on Sunday that all of its planes were serviced in a timely manner and tested before takeoff, and that it had no reason to doubt the professionalism of the pilot or crew of the crashed jet.