Bank of America has agreed to turn over more documents to a congressional probe of its purchase of troubled investment bank Merrill Lynch, although some company material remains under wraps for now, a senior lawmaker said on Tuesday.

After a meeting between a bank executive and the chairman of the House oversight committee, Bank of America will continue to assert attorney-client privilege for some documents but must provide a privilege log the panel can review.

House Oversight and Government Reform Committee Chairman Adolphus Towns said the meeting with global chief strategy and marketing officer Anne Finucane was constructive and his panel would review the log to determine which documents are critical to its investigation.

The panel is looking at the disclosure of pre-merger losses at the investment bank, what funding commitments the U.S. government made prior to the deal, and what legal basis the bank may have had for backing out of the Merrill deal.

An aide to Towns on Monday said a subpoena might be needed to get the documents sought, after the bank missed a deadline imposed by the lawmaker.

But the statement released by Towns on Tuesday did not mention any plans for a subpoena.

Some lawmakers believe Bank of America was forced by the U.S. Treasury and the Federal Reserve to complete the Merrill deal as part of efforts to prop up the banking system during last year's financial crisis.

Others are critical of Bank of America for not giving more information to shareholders about Merrill's financial condition and for letting Merrill pay bonuses before the deal was completed on January 1.

Bank of America is defending itself on multiple fronts over the Merrill deal, including shareholder lawsuits and a threat by New York Attorney General Andrew Cuomo to file civil charges against top executives.

The Securities and Exchange Commission has said it could pursue additional charges against the bank, after a federal judge last week rejected a $33-million settlement between the bank and the commission over whether shareholders were misled about the bonuses.

The bank announced Monday it would exit a $118-billion asset-guarantee program it entered with the U.S. government on the heels of the Merrill Lynch purchase, paying a $425-million exit fee.

(Reporting by Kim Dixon: Editing by Tim Dobbyn)

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