The report charges that these companies paid Saddam Hussein's regime a staggering total of $1.8 billion in surcharges and kickbacks under the humanitarian program, which ran from 1996 to 2002 to help the Iraqi population through the sanctions imposed on their country.
In exchange, the report says they received a large share of the oil-for-food contracts awarded by Hussein's government.
According to its findings, Russia tops the list of countries that illegally profited from oil-and-food contracts, followed closely by France. Both countries had consistently called for easing international sanctions on Iraq.
Leading Russian oil firms such as Alfa Ekho, LUKoil, Zarubezhneft, and Tyumen Oil Company; several prominent politicians; and the Russian Orthodox Church were among the entities named by the commission.
But the report has had little impact in Russia, where it has received only limited, if any, coverage on television and in the press.
The first official reaction came today, when Foreign Minister Sergei Lavrov expressed skepticism about the report.
Russian news agencies quoted Lavrov as saying he was in touch several times with the commission but that "in a number of cases the documents they showed us were fake, in particular the signatures of Russian officials."
Lavrov added that part of the information published by the commission was not backed up by any documented evidence.
Volcker's commission says Russian companies have not provided any information refuting the records submitted to them by the commission.
RFE/RL's Russian Service contacted LUKoil, a major Russian oil firm cited in the report.
A spokesman, Dmitrii Dolgov, said the report did not offer any evidence of violations committed by LUKoil under the oil-for-food program and he suggested that the Volcker report was an attempt by the UN to clear itself of responsibility.
"When we took part in it [the program] at various stages, it happened in line with Russian legislation and UN conditions," Dolgov said. "We allow ourselves to note that, some time ago, a range of rather high-ranking UN officials were proved to have been involved in some of the abuse during the program. So this creates the impression that the authors of the report and UN officials want to shift the blame of this organization on others."
According to the commission, Russia contracted for about $19.3 billion in oil under the program -- which would account for 30 percent of all oil sales from Iraq under the program.
The bulk of the oil was allegedly allocated to major oil firms. But some was also distributed to several political parties, social organizations such as the Russian Union of Officers, and to the Russian Orthodox Church.
According to the report, the Communist Party was allocated 125 million barrels of Iraqi oil through an organization called the Foundation for Friendship with People of Arab States, an operation that allegedly personally involved the head of the party, Gennadii Zyuganov.
The report also claims 73 million barrels were allocated in the name of Vladimir Zhirinovskii, the leader of the Liberal Democratic Party (LDPR). It says Iraq gave Zhirinovskii oil because it thought he was in a position to lobby for political decisions favorable to Baghdad.
Zhirinovskii has publicly denied profiting from Iraqi oil contracts, and the deputy leader of the LDPR, Aleksei Mitrofanov, today dismissed the accusations as "nonsense."
He branded the report as an attempt by the United States to punish those who supported Hussein's regime.
"I think the report was made under the pressure of the United States," Mitrofanov said. "The U.S. is taking revenge on the United Nations for its position before the start of the war in Iraq. It is trying to compromise all those who supported the Iraqi regime. It is not a secret to anyone that we [LDPR] supported Saddam Hussein. But there were no illegal deals. A political party is not an oil firm, it doesn't buy oil or sell food."
Aleksandr Voloshin, who at the time served as chief of staff of the presidential administration, also figured in the list of culprits for allegedly receiving 4.3 million barrels of oil. He, too, has vehemently denied any wrongdoing.
The commission charges that Russia sought to hinder its investigation by failing to provide access to employees of the Industry and Energy Ministry, which coordinated oil purchases by Russian companies under the program.
It says the government claimed that employees and records linked to the oil-for-food program could not be identified due to the reorganization of the Industry and Energy Ministry.