"We are very pleased that Iran and Russia continue cooperation in strengthening peace and security, as it will bear fruit not only in the region but also on the worldwide stage", he said at a meeting with his Russian counterpart Sergey Lavrov.
Russia, Iran and Turkey have also been competing for influence and zones of influence in the country.
The three ministers reiterated their commitment to a peaceful resolution of the seven-year war in Syria, and dismissed criticism from some other nations that the Astana negotiations, which the three nations kick-started, were somehow harmful for the UN-sponsored negotiations in Geneva.
The meeting was meant to prepare the groundwork for the ninth round of Astana talks to be held next month in Kazakhstan, which will focus on political and humanitarian issues.
Lavrov said they "set back efforts to promote the political process" and Zarif criticised Washington's "destructive role".
Al-Aridi said: "We have to ask ourselves, is the Assad regime's brutality helping the peace process; are Russian strikes, the regime's bombardment, displacement of Syrian civilians and Moscow's cover-up of the regime's crimes helping the peace process?"
Lavrov said the recent US-led missile strikes on Syria "seriously aggravated the situation".
"Our cooperation in the fight against terrorism has been successful".
Russia, Iran and Turkey are the guarantor states in the so-called "Astana process" aimed at ending the violence in Syria. He noted that the White house statement of support for the territorial integrity of Syria is "just words".
Also on Saturday, Iran and Russian Federation slammed Western strikes against the Syrian regime in response to its chemical attack on Douma on April 7.
Russian, Iranian and Turkish foreign ministers on Saturday talked up their successes in brokering a political solution to the Syrian conflict at a meeting in Moscow.
No casualties were reported in the attacks and Russian Federation was warned before the missiles were launced.