The bank said the recovered loot was channelled into Nigeria's budget under the Olusegun Obasanjo administration.
The bank said it played a limited role in the spending of the loot because of the structure of the programme adopted by the government at the time.
The World Bank disclosed this in a letter addressed to a civil society organisation, Socio-Economic Rights and Accountability Project (SERAP).
It said the recovered loots were channelled into Nigeria's budget in line with Olusegun Obasanjo's National Economic Empowerment and Development Strategy (NEEDS).
The bank said, "The funds were returned directly from Switzerland to the Nigerian Government adding that it is committed to helping Nigeria account for the spending of the loots.
"They were programmed into the national budget and utilized by the Nigerian Government in line with its National Economic Empowerment and Development Strategy (NEEDS)."
The financial institution added that the structure of the programme did not allow for the comprehensive audits like the bank would normally do with its own funded projects.
The letter further reads, "As agreed with the Nigerian and Swiss governments, the Bank's role was limited to carrying out an ex-post analysis on their use with a particular focus on their contribution to the NEEDS.
"This was done as part of the public expenditure review carried out jointly by Nigerian government and the Bank under the Country Partnership Strategy. The monitoring and analysis of repatriated funds was undertaken at two levels through: (1) the Bank-led analysis of general budget expenditure trends, and (2) a budget monitoring survey which was a limited field survey of sample projects funded under the budget program and randomly selected from a list of projects provided by the government.
"The budget monitoring survey was conducted by joint teams representing both government agencies and Nigerian civil society organizations. The Bank’s role in this particular case was limited by the design and different from the type of comprehensive audits we can do when funds are spent in projects supported by the Bank. We would welcome the opportunity to meet with you to explain the Bank’s role in this matter in the near future.
"We do share your deep commitment to fighting corruption and promoting transparency and accountability. These are key ingredients to successful development and economic well-being.
"We believe that the work organizations like SERAP are doing is critical to achieve our common goal of improving the lives of people in Nigeria and beyond."
Abacha was Nigeria's military head of state from 1993 to 1998.