Rouhani made the call in separate messages to Bangladeshi President Muhammad Abdul Hamid, Montenegro President Filip Vujanovic and Indonesian Speaker Marzuki Ali on Monday, in which he thanked them for congratulating him on his win in the June 14 election.
Also in his message, Rouhani expressed the hope that cooperation between Iran and the aforementioned countries would increase during his presidency.
He also called for strengthening regional cooperation between Iran and Bangladesh.
Iran and Bangladesh agreed to further increase their economic ties as the two countries' fifth joint economic commission meeting wrapped up in Dhaka mid May.
Iran and Bangladesh signed an economic cooperation agreement in a special ceremony in Dhaka at the time.
The ceremony was held on the sidelines of the two countries' economic commission meeting and was attended by Iranian Minister of Industry, Mines and Trade Mehdi Qazanfari and Bangladeshi Finance Minister Abul Maal Abdul Muhith.