Mr. Putin reiterated the Kremlin position that American forces have no legal right to be in Syria, in that they were neither invited by Damascus, as the Russian forces were, nor authorized by the United Nations Security Council.

The American decision to withdraw represented at least a tactical victory for Mr. Putin, who intervened in Syria in September 2015 with the primary goal of re-establishing Russia as a power to be reckoned with in the Middle East, analysts said.

“For now, it is really good news for Putin,” said Konstantin von Eggert, a political commentator on the independent Russian TV station Dozhd. “Putin’s main goal from Day 1 of his intervention was to establish himself as the global authority to prevent regime change. In this he has succeeded.”

But Mr. Putin still faces some challenges in Syria. The Islamic State, while mostly lying low, remains a potentially potent guerrilla force in the eastern desert region, he and others noted. With the Americans out of the way, he will inherit that fight, which he largely avoided while propping up Mr. Assad’s control over most of western Syria.

“ISIS is not defeated. I am sure the Russians know that very well,” said Yuri Barmin, a fellow at the Russian International Affairs Council who specializes in Middle Eastern affairs. “If the Americans are not there to fight it, then who will? It will have to be Russia.”

The American presence also helped to glue together a Kurdish-Arab alliance in the east that is likely to unravel in its absence, he said.

The withdrawal could present problems in the western theater in the Syrian conflict as well. Not only will it remove the hurdle preventing Iranian forces from advancing unimpeded down the road from Iraq into Syria, but it could also fuel ambitions within the Syrian and Iranian forces to capture Idlib province, the last holdout of the armed opposition.