The Airbus A321, operated by Russian airline Kogalymavia under the brand name Metrojet, was flying from the Red Sea resort of Sharm el-Sheikh to St Petersburg in Russia when it went down in central Sinai soon after daybreak on Saturday.
It crashed into a mountainous area shortly after losing radar contact near cruising altitude.
A militant group affiliated to Islamic State in Egypt, Sinai Province, said in a statement it had brought down the plane "in response to Russian airstrikes that killed hundreds of Muslims on Syrian land", but Russia's Transport Minister Maxim Sokolov told Interfax news agency the claim "can't be considered accurate".
Egyptian Prime Minister Sherif Ismail told a news conference on Saturday that there did not appear to be any unusual activity behind the crash but that the facts would not be clear until further investigations had been carried out.
At least 163 bodies had already been recovered and transported to various hospitals including Zeinhom morgue in Cairo, according to a cabinet statement.
Search efforts resumed at the crash site early on Sunday morning and Russian experts were already at the site helping to recover bodies and begin investigations into the cause.Russian investigators had already visited the morgue, a security source said.
Russia, an ally of Syrian President Bashar al-Assad, launched air raids against opposition groups in Syria including Islamic State on September 30.
Islamic State, the ultra-hardline group that controls large swathes of Iraq and Syria, has called for a holy war against both Russia and the United States in response to airstrikes on its fighters in Syria.
Emergency services and aviation specialists searched the wreckage on Saturday for any clues to the crash. Both black boxes had been recovered, Egypt's civil aviation minister said.
The Russian flag could be seen flying at half-staff over the Russian embassy in Cairo today morning.
The passengers included 214 Russians and three Ukrainians.
Sinai is the scene of an insurgency by militants close to Islamic State, who have killed hundreds of Egyptian soldiers and police and have also attacked Western targets in recent months. Much of the Sinai is a restricted military zone.
Militants in the area are not believed to have missiles capable of hitting a plane at 30,000 feet. Islamic State websites have in the past claimed responsibility for actions that have not been conclusively attributed to them.
Officials say there is no evidence to suggest that a bomb could have brought down the plane.
Two of Europe's largest airlines, Lufthansa and Air France-KLM, said they would avoid flying over the Sinai peninsula while awaiting an explanation on the cause of the crash.