A statement from the Iraqi military’s joint operations command on Saturday said the cooperation had come “with increased Russian concern about the presence of thousands of terrorists from Russia undertaking criminal acts with Daesh (Islamic State).”

The move could give Moscow more sway in the Middle East. It has stepped up its military involvement in Syria in recent weeks while pressing for Damascus to be included in international efforts to fight Islamic State, a demand Washington rejects.

Russia’s engagement in Iraq could mean increased competition for Washington from a Cold War rival as long-time enemy Iran increases its influence through Shi’ite militia allies just four years after the withdrawal of U.S. troops.

Russian news agency Interfax quoted a military diplomatic source in Moscow as saying the Baghdad coordination center would be led on a rotating basis by officers of the four countries, starting with Iraq.