UN Secretary General Kofi Annan has been cleared of wrongdoing over an Iraq oil deal involving his son but a report has queried his handling of the affair.
Volcker's team is due to present his final report this summer
The inquiry, which examined the UN's oil-for-food programme, found "significant" questions over the integrity of Kojo Annan's dealings.
It found insufficient evidence to show the father was aware of his son's work with a contractor.
But the UN boss was faulted over an "inadequate" inquiry into the affair.
The UN leader said he was happy with the findings of the interim report and he brushed aside a reporter's question about whether he would resign with the words, "Hell, no".
"I have lots of work to do and I am going to go ahead and do it," he said.
The BBC's Jonathan Beale reports from New York that while Kofi Annan and his staff will claim he has been exonerated, they still face the difficult task of restoring confidence in him and the UN.
The contractor, Swiss firm Cotecna, was hired by the UN to verify goods coming into Iraq.
Kojo Annan, who was a trainee with the firm from 1995 to 1998, continued to be paid a salary until February 2004.
I love my son and always expected the highest standards of integrity from him
Former US Federal Reserve chairman Paul Volcker, who leads the Independent Inquiry Committee (IIC), presented the interim report at the UN in New York.
The final version of the report is not due until June.
"There is no evidence that the selection of Cotecna in 1998 was subject to any affirmative or improper influence of the secretary general," the IIC report said.
However, a UN inquiry initiated by the secretary general was "inadequate [with] no referral to the UN departments carrying the responsibility for thorough and independent investigation of such matters".
The IIC found Kojo Annan "intentionally deceived" his father about his "continuing financial relationship" with Cotecna.
"Significant questions remain about Kojo and his actions," the report said.
A lawyer for the younger Annan said earlier that he had "consistently acknowledged that he was not completely candid with his father when the Cotecna-UN contract first attracted publicity".
But the lawyer, William R Taylor, insisted that Kojo had fully co-operated with Mr Volcker's investigation.
The IIC report also raised questions about Cotecna while noting that it had "generally co-operated" with its work.
The firm has said it was selected fairly for its UN Iraq contract "without political or personal influence of others".
Kofi Annan said he had been "deeply saddened" by the findings against his son and "particularly by the fact [Kojo] had failed to co-operate fully with the inquiry".
"I love my son and always expected the highest standards of integrity from him," he said.