President Rouhani made the remarks in a trilateral meeting with his Russian and Azeri counterparts Vladimir Putin and Ilham Aliyev in Tehran on Wednesday.
Tehran welcomes any idea leading to bolstering of relations and cooperation with Moscow and Baku, he said.
"In such arrangements all should set their approaches on a win-win strategy," Rouhani added.
Iran believes that the present interaction between Iran, Russia and Azerbaijan will go beyond bilateral relations or even a trilateral format and will not only lead to various political, security, cultural and economic cooperation, will also create new opportunities through convergence to deal with all regional challenges, he said.
Appreciating his Russian and Azeri counterparts for attending the meeting, President Rouhani said, "I believe that the meeting will be a significant move in broadening cooperation between these three countries more than before and will draw out a very promising future in deepening and bolstering ties between the parties."
There is no doubt that the firm determination of the three capitals to hold the second trilateral meeting in Tehran was a positive initiative for exchanging the three sides views on different issues and following up their relations in a way which will serve their common interests, he said.
Iran's economy is capable to register a remarkable growth of on-trillion-dollar within coming 20 years and be regarded as one of the promising economic hubs in the world, President Rouhani said.
To attain the goal, it will be very vital to broaden cooperation with the neighboring countries, he said.
"Iran is ready to broaden interaction and cooperation with the Russian federation and Republic of Azerbaijan in various cultural, historical affinities, ample of God-given natural resources, geographic location and common and political will of their leaders."
"Tehran and Moscow are to broaden the scope of bilateral cooperation in nuclear related activities, implementation of the JCPOA, fight against terrorism, dealing with Syrian crises, broadening economic cooperation," President Rouhani said.
Presently unprecedented challenges such as terrorism and extremism along with destructive interferences of trans-regional powers are common threats against regional countries and cooperation and consultation of regional states are the only solution to solve those problems, he said.
"Tehran welcomes expansion of bilateral cooperation with the Russian Federation in dealing with such challenges,” President Rouhani said.
Putin and Aliyev arrived in Tehran on Wednesday, heading a high-ranking delegation, to hold talks with the Iranian officials on ways to further develop ties and cooperation.
Presidents of Iran, Russian and Azerbaijan held the second round of trilateral talks in the Iranian capital on Wednesday.
The first round of talks between President Hassan Rouhani, President Vladimir Putin and President Ilham Aliyev was held in Baku in August 2016.