The International Finance Corporation [IRC] plans to take a 20% share - valued at $2m (£1.3m) - in an Iranian leasing company. It will also lend the company a further $3m.
But the World Bank's biggest shareholder, the United States, is expected to oppose a deal. It regards Iran as a member of the so-called axis of evil for allegedly trying to develop weapons of mass destruction.
The IFC says it hopes the project, which is co-sponsored by Iran's Karafarin Bank and France's Natexis Banque Populaires, will help to develop the country's leasing sector and so indirectly help Iran's economic development.
Strong opposition
The IRC says on its website that the leasing company, Karafin Leasing, will focus on medium-term equipment leases with particular emphasis on servicing the needs of small and medium sized companies.
"This project has been conceived in response to the shortage of term finance to the private sector in Iran," the IRC said.
Lending to countries branded as members of the "axis of evil" faces strong opposition in the US Congress. And Congress controls the amount of government money given to the World Bank and the IFC.
The US voted against the last investment the World Bank made in Iran in May 2000 - a $232m loan for health and sewerage projects.
The World Bank plans to lend Iran $755m over the next two years.
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