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He also warned Israel and Iran not to use Syria for their proxy conflict
The Kremlin suggested that it is difficult to work with the Americans under such circumstances.
Russian President Vladimir Putin praised historic and strategic ties with Egypt.
Putin warned that reforms would not be easy and would require "compromise and concessions" from all parties to the conflict.
Assad arrived in Sochi on Tuesday to coordinate peace initiatives ahead of a summit involving Iran, Russia and Turkey.
Washington has accused Moscow of "obstructing justice", but Russia says UN mechanisms on Syria have become tools of the West.
The joint statement said the political process should be for all Syrians, including those displaced by the civil war.
The US has been routinely invited to the Astana talks, but has only been represented by low-level delegations.
The Islamic State now controls less than eight per cent of Syrian territory, Russian commanders say.
The Lebanese army has also been defeating IS forces on its side of the border near the town of Ras Baalbak.