Kudrin and the Iraqi Foreign Minister, Hoshyar Zebari, signed an agreement on the cancellation of the debt in Moscow.
Iraq's debt to Russia stood at $12.9 billion.
Kudrin said the debt will be cancelled in several stages. In the first stage, 65% of the debt will be written off. The remaining $4.5 billion will be cancelled in two stages, subject to further negotiations.
Earlier in the day, Russian Foreign Minister Sergei Lavrov and Zebari signed a memorandum of cooperation in the trade, economic, scientific and technical spheres.
"The memorandum, which we have just signed, will open doors for Russia for full-fledged participation in all projects and tenders to be held in Iraq," Zebari said.
Lavrov said Russian companies intend to become actively involved in the reconstruction effort in Iraq.
"We are counting on long-term joint projects in the oil and natural gas and energy sectors," he said.
Russia could invest as much as $4 billion in Iraq, Kudrin went on.
The Iraqi government expected the intergovernmental deal to be signed before the end of 2007. Some media said the delay was due to Iraq's cancelation of a 1997 contract with Russian oil company LUKoil on the West Qurna-2 oil field, one of Iraq's richest. But both countries' authorities dismissed the allegations.
Zebari said last September that his country could offer Russian oil and gas companies considerable advantages as regarded operations in Iraq, but ruled out that this could be linked to the debt settlement issue.
