Speaking in a provincial meeting, broadcast live on State TV Thursday, Rouhani called the decision "a positive development."
Iran had initially been hesitant to cut its oil production. The country was eager to make up lost revenue after international economic sanctions were lifted in the wake of a landmark nuclear deal.
Tehran agreed to limit its production to just under 3.8 million barrels per day. Iran's arch-rival Saudi Arabia agreed to the largest production cuts, chopping nearly half a million barrels from its current 10.5-million-barrel daily output.