Since Wednesday, several countries including Belgium, the Netherlands and Germany have restricted travel to Sharm el-Sheikh.
The travel chaos has grown after French aviation officials have told media the Russian plane crash in Egypt last week was not due to technical failures.
Other French officials said the flight data recorder suggested a "violent, sudden" explosion caused the crash, killing all 224 people on board.
Intercepted militant calls indicate a bomb was put in the hold before take-off, according to UK officials.
Militants linked to the Islamic State group (Isis) say they downed the plane.
The Metrojet Airbus A321 was flying from Sharm el-Sheikh to St Petersburg when it came down in Sinai last Saturday. Most of the victims were Russian.
French air accident investigators cited by AFP said the flight data recorder had shown that "everything was normal during the flight, absolutely normal, and suddenly there was nothing". A similar conclusion was drawn by another investigator speaking to France 2 television.
The American network NBC, quoting unnamed US officials, said that communications had been intercepted between IS officials in Syria and people on Sinai about how the jet had been brought down.
"They were clearly celebrating," NBC quoted the official as saying.
Putin had a telephone conversation with Egyptian President Abdul Fattah al-Sisi, agreeing to continue "active co-operation" on flight safety, the Kremlin said.
The Russian decision to suspend flights to Egypt is a major blow to tourism, which is a lifeline to the Egyptian economy.
More than 30 per cent of the tourists who visit Egypt each year come from Russia.
The tourism industry has been struggling since the revolution in 2011, due to political uncertainty.
In recent months, there was some sense of stability so things had began to improve.
The US has announced it is stepping up security screening of items on US-bound flights from some airports in the Middle East. The Homeland Security statement did not say which airports it was targeting.
Tourism contributed more than 12 per cent to Egypt's economy in 2013 and the latest measures will hit it hard, analysts say.