Putin and Assad met at the command post to hear military reports on various regions of Syria, Peskov added.
Meanwhile Kremlin spokesman Dmitry Peskov told Russian state news agency RIA that bilateral negotiations had taken place.
While the official statements made no mention of the US killing of Iran's Revolutionary Guard General Qassem Soleimani on Friday, the timing was conspicuous.
As the head of the elite Quds Force, a branch of the Islamic Revolutionary Guards Corps, Soleimani had for years wielded his country's influence across the wider Middle East, strengthening Shia militias from Lebanon to Iraq and coming to the aid of Tehran's allies, like Bashar Al Assad in Syria.
Russian and Iranian support has helped Assad win back almost all the territory lost to rebels who tried to overthrow him in a civil war that grew out of a crackdown on opposition protests almost nine years ago.
The last time Putin visited Syria was in 2017 when he declared that mission for Russian troops has been accomplished.
Putin wanted to make clear that Russian Federation won't tolerate Iranian reprisals from Syrian territory, sources report.
He said that Assad thanked Putin for the visit and expressed appreciation for Moscow's help during the Syrian civil war.
Syrian President Bashar al-Assad, backed by Russian Federation and Iran, has vowed to recapture Idlib, the last rebel-held swathe of territory.
Mr Putin is expected to travel to Turkey next, the other key broker in a conflict that has left more than 380,000 people dead and displaced half the country's population. My colleague also stressed: "Turkey will raise questions of deoccupation of Crimea and release of all UA citizens illegally detained in Russian Federation & occupied territories during Putin's visit today", Prystaiko wrote on Twitter on January 8, 2020.
While the timing of this visit could be related to unrest in Iran, it could also be a show of support for Assad before Putin is scheduled to meet with Erdogan in Istanbul on Wednesday.
It was Putin's first visit to Damascus and only his second visit to Syria since Russian Federation began offering military support to Syrian government forces in its long-running conflict.
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