More than 2,000 companies have been accused of making illegal payments to Iraq as part of the UN oil-for-food scandal.
DaimlerChrysler says it cannot comment on the allegations
Chief investigator Paul Volcker said the firms would not necessarily have known they were paying bribes, but that if countries wanted to pursue companies or individuals they would provide information and help as much as possible.
"We want to cooperate with them," he told the BBC. "Now we haven't got a lot of time to do it so I hope they can make a request early."
In Switzerland, criminal proceedings were launched against four un-named people, the economics ministry said on Thursday, and others would be prosecuted if shown to have "behaved illegally".
The Swiss have already fined a Geneva-based
oil-trading company $40,000 (£22,000) for paying kickbacks to Iraq, but refused to name the company.
Some companies paid surcharges after winning oil contracts
Dutch-based oil trader Trafigura, alleged in the report to have bribed sanctions inspectors, responded by saying: "Trafigura Beheer BV absolutely refutes any suggestion that
it was knowingly involved in any breach of the UN
Germany-based car maker DaimlerChrysler is alleged to have paid $7,000 on a contract worth $70,000
It said it could not comment on the claims as US authorities were still carrying out their own investigations.
Weir Group, of Scotland, which makes oil equipment, made $4.5m in illicit payments from 16 contracts, the report found.
Weir has already apologised for making excessive payments to Iraq.
A spokeswoman for Brussels-based Volvo
Construction Equipment, a subsidiary of Swedish-based Volvo Group, denied any knowledge of illegal payments or the UN report.
It is accused of paying $317,000 in extra fees to
on a $6.4m contract.
Mr Volcker has stressed that identifying a company in the report did not necessarily
mean that the firm knowingly made the payments, and that this may have been done through an agent.