The Washington Post quoted Nasir Nouri Mohammed, a spokesman for the Iraq's defense ministry, as saying the decision was made "because all these four countries are involved in fighting terrorism," and that a joint intelligence-sharing center would be set up in Baghdad "in weeks, maybe less."
The move is reported to have caught off guard the administration of U.S. President Barack Obama, which has for more than a year overseen an aerial bombing campaign against the extremists in Iraq and Syria.
"This is not yet coordinated," The New York Times quoted U.S. Secretary of State John Kerry as saying at the start of a meeting in New York with Russian Foreign Minister Sergey V. Lavrov. "I think we have concerns about how we're going to go forward, but that's precisely what we're meeting on to talk about now."
The announcement comes amid a Russian military build-up at an air base in western Syria's Latakia province -- the Alawite heartland of President Assad. Moscow confirmed the presence of Russian military advisers in the country earlier this month.
Russia and Iran have long backed Assad, who has since 2011 been locked in a civil war against a fragmented insurgency of mainly Sunni Arab rebels, including al-Qaida and IS jihadists, but the recent build-up -- as well as Iraq's announcement -- represent a widening role for Russia in the region.
White House Press Secretary Josh Earnest earlier this month said the United States "would welcome constructive Russian support" against IS forces in Iraq and Syria but characterized support for the Assad regime, which the United States opposes, as a "losing bet."
After Bulgaria more than two weeks ago agreed to a request by the United States to ban Russia from using its airspace to shuttle supplies to Assad, Iraq joined Iran in allowing Moscow the use of an air corridor through both countries.
Iran, meanwhile, has supported the Baghdad government by supplying advisers to train Shia militias ever since IS forces took over large swaths of Iraq last year, but U.S. officials assert they have not coordinated with the militias, known as Hashid Shaabi, or Popular Mobilization Committees, when conducting airstrikes in support in Iraqi forces, despite both entities being key to Iraqi victories in places like Tikrit.