"On behalf of the entire Syrian people, I express my gratitude for what you have done," Assad told generals. "We will not forget it."
Assad's opponents, and Western governments, have accused Russia of killing significant numbers of Syrian civilians with its air strikes, allegations Moscow denies.
Putin praised Assad for "fighting terrorism," which he predicted would suffer an "inevitable" defeat in Syria, the Kremlin said.
"It is in our interest to advance the political process... we don't want to look back and we are ready for dialogue with all those who want to come up with a political settlement," Assad said in translated comments.
Putin said he would "consult" world leaders, including US president Donald Trump, on his talks with Assad. Putin's telephone talks with Trump are due on Tuesday, the Kremlin said.
On Wednesday, the presidents of Russia, Turkey and Iran will meet for the first of a series of summits to bring peace in Syria, where regime forces now have an upper hand over rebels and the Islamic State group.
Putin will host Turkey's Recep Tayyip Erdogan and Iran's Hassan Rouhani in Sochi ahead of parallel UN-led talks in Geneva set for November 28.
The meeting - the first such three-way summit between the trio - comes as Ankara, Moscow and Tehran cooperate with increasing intensity on ending the over six-year civil war in Syria that has left 330,000 dead and millions homeless.
The cooperation comes despite Turkey still officially being on an opposite side of the Syria conflict from Russia and Iran, which are key Assad backers.
Turkey has supported rebels seeking Assad's ouster but has muted its criticism of the Syrian regime.
"The open-war phase in the Syria conflict will soon be over and the question of a political solution will become more pressing than before," Russian political analyst Azhdar Kurtov told AFP.
"Russia, Iran and Turkey each have their own interest in Syria. It is clear that they also have disagreements. And they are meeting to try to smooth over these disagreements," he said.
The three countries have backed negotiations in the Kazakh capital Astana that have brought together the representatives of the opposition and the regime seven times this year.
The talks have led the creation of four so-called "de-escalation zones" that have produced a drop in violence, but sporadic fighting and bombardment has continued.
Moscow is now seeking to steer the process, which has so far focused on military questions, in a political direction.
The Sochi summit will help to "relaunch direct negotiations between the Syrian government and the range of the opposition," said Russian Foreign Minister Sergei Lavrov.
"As a victory over Islamic State in Syria... grows closer, there are conditions for the relaunch of political negotiations," he said Friday.
Moscow's military intervention in Syria from 2015 is widely seen as tipping the balance in the conflict.
Since then the Syrian army has reclaimed the ancient city of Palmyra from the Islamic State group and driven rebels out of their northern bastion Aleppo.
This week regime forces ousted the Islamic State group from its last urban stronghold in the country, Albu Kamal, which has changed hands several times.
Previous attempts to end the war have stalled over the question of the fate of Assad.
But Turkey is showing greater flexibility on that issue, even if it remains unlikely that it will officially accept the prospect of the Syrian president remaining in power, said Timur Akhmetov, an Ankara-based Turkey expert at the Russian International Affairs Council.
"For now, to keep a say in the future political negotiations is more important for Turkey than to have Assad departed from power," he told AFP.
The last attempt by Moscow to bring together the regime and the opposition in Russia was coldly received by the rebels and no date has been fixed for a meeting which was originally set for November 18.
Different factions of the Syrian opposition will meet from Wednesday in Riyadh in talks hosted by Saudi Arabia.
The aim of the Saudi-backed High Negotiations Committee is to reach consensus on a strategy for talks in Geneva, which will focus on a new constitution for Syria and fresh elections.
