Speaking to the press afterwards, Dodik said a new time was coming for economic cooperation between the Bosnian Serb entity and Serbia.
Kostunica visited the entity for the first time since Montenegro declared independence from the state union with Serbia last weekend. He said it was agreed today to build a Bosnia-Serbia border crossing at Raca, adding it would be "of mutual benefit".
Dodik refuted all speculation that today's talks addressed the calling of a referendum on the separation of Republika Srpska from Bosnia and Herzegovina.
"We talked about the development of the economy and the advancement of cooperation in this area," he said.
Kostunica also met entity President Dragan Cavic, who said they agreed changes to the a 2001 agreement on special ties between Republika Srpska and the then Federal Republic of Yugoslavia (FRY).
The two officials said it was necessary to take into account the new situation in Serbia, the successor of FRY and later the State Union of Serbia and Montenegro, as well as the fact that in the meantime the entity's Constitution was changed to include a provision on three constituent peoples -- Serbs, Croats and Muslims.