Lavrov organized the talks with Ararat Mirzoyan and Jeyhun Bayramov in Tajikistan’s capital Dushanbe as part of Russia’s apparent efforts to regain the initiative in the peace process.
Moscow accused the European Union and the United States last month of trying to hijack the process and use it in the standoff over Ukraine.
"I hope that today's meeting will make it possible to move forward along the path that was outlined by our leaders," the Russian news agency RIA Novosti quoted Lavrov as saying at the start of the talks held on the sidelines of meeting of top diplomats of ex-Soviet states.
He alluded to the Russian-brokered agreements to stop the 2020 war in Nagorno-Karabakh, open transport links between Armenia and Azerbaijan and demarcate their border.
“We believe that there is a good prospect, a good opportunity to achieve … the full implementation of the tripartite statements in full," Bayramov said, for his part.
In a statement issued after the talks, the Russian Foreign Ministry said the three ministers “reaffirmed the commitment to strict compliance with all provisions” of those agreements. They also discussed planned negotiations on an Armenian-Azerbaijani peace treaty, it said, adding that Moscow is ready to facilitate them.
The trilateral encounter followed Lavrov’s separate talks with Bayramov and Mirzoyan. The latter was reported to tell Lavrov that a newly formed Armenian-Azerbaijani commission on the border demarcation will hold its first session in Moscow next week.
Armenian Prime Minister Nikol Pashinian and Azerbaijani President Ilham Aliyev agreed to set up the commission before the end of April when they met in Brussels on April 6. European Council President Charles Michel, who hosted the summit, said they also plan to “move rapidly” towards negotiating the peace treaty.
Russia responded by accusing the West of trying to sideline it and claim credit for the Armenian-Azerbaijani agreements.
Mirzoyan also indicated in Dushanbe that a Russian-Armenian-Azerbaijani working group dealing with economic and transport issues will resume its work in Moscow May 16 after a nearly five-month hiatus.
The group’s Russian co-chair, Deputy Prime Minister Alexei Overchuk, visited Yerevan and met with Pashinian on Thursday.