Putin met last week with U.S. President Barack Obama during a meeting in St. Petersburg of the world's top 20 economic powers. Obama is working to generate support for a military strike on Syria, something his Russian counterpart opposes.
Muallem issued a statement to Putin expressing his gratitude for strong bilateral ties.
"[The Syrian] president asked me to pass his thanks to Putin for his stance during and after the G20 summit," he was quoted by state news agency RIA Novosti as saying Monday.
Russia counts Syria as a top ally and military consumer. Putin said allegations the Syrian regime used chemical weapons on civilians in August was a rebel move to court international favor for a strike on government forces.
Russian Foreign Minister Sergei Lavrov said in a joint press conference with his Syrian counterpart the Kremlin was working to bring all parties to the Syrian conflict to the negotiating table.
"We do not rule out inviting to Moscow all those interested in peace in Syria, all those interested in a political solution, those who reject a military scenario, including, of course, [military] intervention," he said Monday.