Mr Putin noted that shared efforts by Moscow and Tehran have played a key role in “helping the Syrian government overcome the threats posed by international terrorism”.
Russia and Iran have joined forces to shore up Syrian President Bashar Assad, helping his government reclaim most of the country’s territory after a devastating civil war.
Moscow has performed a delicate balancing act, maintaining contacts with Iran while also building warm relations with Israel, which views the Iranian presence in Syria as a red line.
In 2018, Russia struck a deal with Iran to keep its fighters away from the Golan Heights to accommodate Israeli concerns about the Iranian entrenchment in Syria.
Russia also has actively taken part in international talks aimed at salvaging Iran’s tattered 2015 nuclear deal with world powers.
The US withdrew from the accord in 2018 under then-president Donald Trump, while President Joe Biden has signaled he wants to rejoin the deal.
The 2015 agreement was intended to rein in Iran’s nuclear programme in return for loosened economic sanctions.
Britain, France, Germany, Russia and China are still part of the agreement.
During the talks on Wednesday, Mr Putin also told Mr Raisi he would like to discuss their shared concerns about the situation in Afghanistan.
Mr Raisi, a conservative cleric elected last year, said Iran was willing to expand co-operation with Russia in the political, economic, defence and security spheres, and in space exploration.
Last month, Iran launched a rocket into space with a satellite carrier bearing three devices, a move intended to show the nation’s growing technological prowess amid a standoff in talks on curtailing its nuclear programme.
Mr Raisi told Mr Putin Iran has drafted a proposed agreement on “strategic co-operation” between the countries for the next 20 years.
“We would like to develop strong and multifaceted ties with Russia,” Mr Raisi said. “These relations should be durable and strategic.”