The fate of the two pilots who ejected from the downed plane is unclear. Turkey had objected last week that Russia was bombing Turkmen rebels in Syria.
The Metrojet jet was downed over Egypt's Sinai Peninsula on Oct. 31, an attack claimed by Islamic State. Russian officials say there is growing consensus with Western powers on fighting Islamist terrorism.
The Syrian president's visit to Moscow, his first known visit abroad since the civil war began, indicates confidence in how the conflict is developing now that Russia has entered the fray.