Prime Minister David Cameron has told Vladimir Putin that Britain "shared the pain and grief" of the Russian people after the plane crash in Egypt which killed more than 220 people.
Mr Cameron called the Russian president to "express his condolences" this morning after the plane bound for St Petersburg crashed in the Sinai Peninsula, a Downing Street 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.
"The president welcomed this offer, noting that Russian experts were already in Sinai and working with the Egyptians and that analysis of the black box would be the next step."
Mr Putin thanked Mr Cameron for the call ahead of their meeting at the G20 in Turkey later this month, the spokesman added.
All 224 people on board the plane died in Saturday's crash, which happened 23 minutes after the aircraft took off from the popular Egyptian resort of Sharm el-Sheikh.
Nearly all of the victims were Russian, while Ukraine said four of its citizens were passengers.
Twenty-five children were on board the Airbus A321-200, which was operated by Moscow-based Metrojet airline, and there were seven crew members.
A local affiliate of the extremist Islamic State group (IS) said it "brought down" the plane, but Russia's transport minister has dismissed the claim.
Budget airline easyJet said it will "actively review" the safety of flights to Egypt following the crash.
Emirates, Lufthansa and Air France have said they have stopped flying over the Sinai Peninsula until more is known about the cause of the crash.
But easyJet said it will continue to fly holidaymakers to the popular resort of Sharm el-Sheikh "as planned".
British Airways said it could not comment on "exact flight routes".
An easyJet spokesman said: "EasyJet can confirm that following the incident in Egyptian airspace involving a Russian airline it is currently assessing the situation and taking advice from all the relevant authorities.
"Based on the information received to date, easyJet plans to continue to operate to Egypt to carry holidaymakers as planned to and from Sharm el-Sheikh and Hurghada but will continue to actively review the situation.
"Those passengers who don't want to fly will be offered an alternative flight or a flight voucher.
"The safety of our customers and crew is our highest priority."
Asked whether BA flights would fly over the Sinai following the crash, a BA spokesman said: "We never discuss exact flight routes. However we would never fly a route unless it's safe to do so.
"The safety and security of our customers and crew is always our number one priority.
"Our safety team continually liaises with the appropriate authorities around the world, and we conduct very detailed risk assessments into every route we operate."
It is understood that airlines continuing to fly over the Sinai will only do so at a height that is considered safe.
Foreign Secretary Philip Hammond has spoken to Russian foreign minister Sergei Lavrov to express his sympathies following the crash, the Foreign Office said.