Official news agency SANA said Assad and Alawi discussed "the ideas proposed at the regional and international levels to help resolve the crisis in Syria".
"The Syrian people ... welcome the sultanate's sincere efforts to help Syrians realise their aspirations in a way that preserves the country's sovereignty and territorial integrity," Assad said.
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Alawi, for his part, was quoted as saying Oman was eager to preserve Syria's "unity and stability" and would continue its efforts to find a political solution to the conflict.
Oman has not cut diplomatic or political ties to Damascus, unlike other Arab countries in the Gulf.
In August, Syria's top diplomat Walid Muallem met with Alawi in Muscat, in the foreign minister's first visit to the Gulf since the brutal war began in 2011.
Oman's discreet diplomacy has contributed to several breakthroughs this year, including the release in August of a French hostage held in Yemen and the July nuclear accord between Iran and world powers.