Shuvayev said Russian firms were in talks on participation in several sectors of Iraq's economy.
"Yes, it's all happening rather spontaneously. It's not like it's a planned offensive," he said. "Talks are under way. ... There is readiness from both sides (to develop relations)."
Moscow bolstered its influence after Russian oil company LUKOIL, part of a broader consortium, sealed a 20-year deal to develop the second phase of West Qurna last year.
A separate Gazprom Neft-led group aims to start drilling in Badrah oilfield next year.
Russia's No. 3 oil company, TNK-BP, qualified to bid in next week's auction for three gas fields, an Iraqi official said this week.
Shuvayev said Moscow was realistic about its role in Iraq.
"The current government is completely different, so returning (to Saddam-era ties) would not be possible," he said.
"Russia was against the U.S. operation, not because we were Saddam's advocates, even though, and we are not hiding this, we had a well developed system of cooperation with the previous regime."
He said Iraqi-Russian connections have historically been close, pointing to the abundance of Soviet-designed AK-47 automatic rifles on the streets as an example.
"Only one out of 10 rifles you see at checkpoints around here is U.S.-made," he said, smiling. "There is a certain psychological link and overturning it completely is not always effective."