The minister spoke at a news conference in Moscow following talks with the Russian leadership.
"The doors are open for Russian companies to work in Iraq, but on conditions equal to other companies," Zebari told a news conference.
Russia wrote off $12 billion, or 93%, of Iraq's debt to Russia on Monday, a move widely rumored to be aimed at securing lucrative oil contracts.
The minister said a host of Russian firms work in Iraq, mainly in the electricity sphere, on contracts worth an overall $500 million.
He added that all Russian companies wishing to work in Iraq must be registered in line with laws and guidelines developed by Iraq's oil ministry and that Baghdad has asked Russian companies to do so as soon as possible.
The minister said a bilateral commission will be established to look into contracts suspended since the fall of Saddam Hussein's regime, which he said, would demonstrate his country is not trying to avoid issues, "originating from former obligations."
"The commission will also consider contracts with LUKoil and other Russian companies," he added.
Iraq cancelled a 1997 contract with oil company LUKoil on the West Qurna-2 oil field, one of Iraq's richest, in 2002.
Zebari said last September that his country could offer Russian oil and gas companies considerable advantages to operate in Iraq, but ruled out that this was linked to the debt settlement issue.
