Aleksandr Bortnikov, head of the Federal Security Bureau (FSB), was addressing a Russian anti-terror committee meeting in Moscow.
UK investigators believe a bomb was put in the plane's hold prior to take-off, killing all 224 people on board.
The UK has suspended flights to Sharm el-Sheikh and is bringing Britons home.
Russia should suspend all flights to Egypt until the cause of the Sinai crash is determined, the head of Russian security has suggested.