The two companies were among 2,000 firms listed by investigator Paul Volcker, who presented his findings in New York on Thursday.
The bribes are alleged to have been made within the framework of the now scandal-ridden Oil for Food programme. Saddam Hussein gained up to $1.8 billion in bribes during the sanctions era.
Volvo has been implicated by the actions of its subsidiary Volvo CE, which makes construction equipment. Swedish engineering company Atlas Copco is also among those accused.
During the years of sanctions in Iraq, the Ministry of Foreign Affairs in Stockholm handled around 40 applications per year for licences to export to the country.
According to a memorandum from last summer, compiled by the ministry’s legal secretariat for EU issues, there were no breaches of the rules of the Oil for Food programme uncovered except for one case in 2001, in which two people were found exporting to Iraq without a licence.
In a list compiled as the programme was ending in November 2003 there were 28 applications for export licences in 2003, of which 6 were not approved. In that year, Sweden exported goods to Iraq worth 159.2 million kronor. These included humanitarian goods such as pumps, medicines, ambulances, water purifiers and agricultural equipment.
In 2004 the value of Sweden’s exports to Iraq had risen to 665.7 million kronor, according to Statistics Sweden.