The statement came before the European Council had officially extended its economic sanctions against the Black Sea peninsula of Crimea and the city of Sevastopol until June 2016.
A decision to prolong the restrictive anti-Russia measures is expected to be made during a EU foreign ministers meeting on Sunday, June 21.
"Caricature" Western sanctions against Russia are "obviously not without consequences. Not just for Russia, but also for the European economy," Dodik told Sputnik on the sidelines of the St. Petersburg International Economic Forum (SPIEF).
Republika Srpska, which translates as Serbian Republic, is an autonomous entity within Bosnia and Herzegovina.
According to Dodik, strong regional and global partnership options are available to Russia despite the sanctions regime.
"Republika Srpska is interested in any form of cooperation with BRICS. As one of the two entities within Bosnia and Herzegovina, it was Republika Srpska that did not approve the country joining the sanctions against Russia," Dodik said.
"This new geopolitical phenomenon [BRICS] will allow the world to develop more dynamically on the principle of competition and not monopoly," Dodik told Sputnik.
Republika Srpska wants to take part in the Turkish Stream gas pipeline, he said.
Having blocked the construction of the South Stream pipeline, the EU acted "cynically" towards Republika Srpska, Dodik said.
"It is clear that Europe does not want us to receive gas like Germany does via the Nord Stream pipeline," he claimed. "But we did not ask for anything beyond the Nord Stream project."
"Russia and Greece signed a memorandum. It is an important step forward. Now the matter depends on Macedonia’s decision. As far as I know, Serbia will participate in the Turkish Stream project," Dodik said.
Republika Srpska will surely join the project, he concluded.