Both Aliyev and Pashinyan arrived in Moscow on Monday morning for the negotiations were initiated by Putin.
"We may today be satisfied to state that trilateral agreements are being consistently implemented", he said, adding that the situation in the disputed region is stable.
The Russian President also noted that a trilateral group will be set up to control further restoration of Nagorno-Karabakh's economy.
"Special attention should be paid to unblocking economic, trade and transport links in the region, and opening borders. It is assumed that a special trilateral working group, chaired by Russian, Azerbaijani and Armenian deputy prime ministers, will focus on these issues," Putin said.
According to Putin, since 14 November, over 48,000 people have returned to Karabakh.
The decades-long Nagorno-Karabakh conflict between Baku and Yerevan flared up in late September, resulting in military and civilian casualties on both sides. The hostilities ended after the sides agreed to a Moscow-brokered ceasefire on 9 November, leading to the deployment of the Russian peacekeepers to the region.