Shuvayev said the Russian firms looked mainly at non-oil projects to avoid friction with the federal government but some talks had also taken place in the energy sector.
"Some affiliated companies have tried to do something there but I have not heard of any great success," he said.
According to the Reuters report, Russia had a cosy relationship with Iraqi dictator Saddam Hussein, supplying him with weapons and winning the right to develop West Qurna -- one of the world's biggest oilfields.
Saddam tore up that deal in 2002, months before the U.S. invasion that ousted him, saying the Russians had failed to live up to their side of the contract.
Moscow is now looking for ways back into Iraq's war-battered economy, which needs investment in practically every sector.
While most Iraqis are struggling to overcome the effects of a seven-year war, the semi-autonomous Kurdish region remains stable and many investors are keen to tap its vast oilfields. Some also see it as an entry point for the rest of Iraq.