"Saddam Hussein was able to loot billions of (dollars of) Iraqi people's money under the supervision of the United Nations," Intifadh Qanbar, a spokesman for council member Ahmad Chalabi, told a news conference.
He said the council would hire international legal and accountancy firms to help the inquiry investigate "all personalities, companies, families, leaders, politicians all over the world who received these bribes".
Media reports have alleged government officials, foreign firms and a senior UN official were among those who profited illegally from the humanitarian programme.
Chalabi heads the US-backed council's finance committee, which has been making preliminary investigations.
The United Nations has already begun an in-house probe of its staff and UN Secretary-General Kofi Annan last week asked members of the Security Council for their support in a second independent, high-level inquiry into the allegations.
Annan has been under pressure to conduct an inquiry from US officials searching for Saddam's suspected hidden assets.
One name on a published list was Benon Sevan, who ran the UN programme that began in December 1996 and ended a year ago.
The inquiry will investigate "all personalities, companies, families, leaders, politicians all over the world who received these bribes"
spokesman for Ahmad Chalabi, IGC
Oil companies chosen by Iraq put money into a UN escrow (third party) account out of which suppliers of civilian goods were paid to ease the impact of 1991 Gulf war trade sanctions on Iraqis.
Sevan has denied the allegations and UN officials have said they have not been given any documents.
Annan, in his letter to Security Council members on Friday, said the media allegations must be addressed "to bring to light the truth and prevent an erosion of trust and hope that the international community has invested in the organisation".
UN officials say any probe would need to look at foreign companies, suppliers, middle men who bought the oil and the French bank BNP-Paribas, which handled the UN-Iraq account.
Annan has been under pressure
to conduct an internal UN probe
The oil-for-food programme handled more than $65 billion in funds for food, medicine and other civilian goods. It was shut down last year after the US-led invasion that toppled Saddam.
The US General Accounting Office (GA0), an inter-agency body headed by the treasury, is trying to locate and seize $10 billion to $40 billion in estimated hidden Iraqi assets.
The GAO said in a report last week that Saddam acquired $5.7 billion of these assets from the proceeds of oil smuggled through Syria, Jordan, Turkey and elsewhere.