Corrects attribution of ninth paragraph quote to Representative Cummings, not Schapiro, as earlier sent

WASHINGTON - The head of the U.S. Securities and Exchange Commission said she wished the SEC's former top lawyer had removed himself from the agency's work on the epic Bernard Madoff fraud.

In an affair that is undermining the agency's pleas for more funding, SEC Chairman Mary Schapiro told a congressional panel that, in hindsight, former SEC General Counsel David Becker's Madoff ties should have been handled differently.

I wish that Mr. Becker had recused himself, Schapiro said on Thursday at the third of a trio of hearings on Capitol Hill where she and other officials were grilled over Becker, the Madoff episode generally, and the SEC's budget.

At a time when the SEC is laboring to meet tight deadlines for implementation of dozens of new financial regulations under 2010's Dodd-Frank Wall Street reforms, the Becker episode is proving to be a major distraction.

The matter may be one of the greatest challenges to the SEC's credibility since Bernard Madoff managed to dupe so many Americans, House Oversight Committee Chairman Darrell Issa, a Republican, said at the final hearing of the day.

Becker left the SEC at the end of February, as previously planned, but has told lawmakers he was advised by the agency's ethics counsel that he could participate in Madoff matters even though he disclosed inheriting Madoff funds from his mother.

Schapiro said she was informed that Becker's mother had a Madoff account, but could not recall whether Becker specifically told her that he inherited money from that account. Madoff trustee Irving Picard is now suing Becker and his brothers to claw back $1.5 million in phony profits from their mother's estate.

Regardless, Schapiro says it was her responsibility to see around the next corner on such matters, especially when the public's trust in the SEC could be on the line.

The sad part about it is one of these little incidents can almost destroy that trust, Representative Elijah Cummings told the afternoon hearing.

Republicans opposed to giving the SEC more money, and opposed to the new rules it is implementing in response to the 2007-2009 financial crisis, seized on the Becker case.

Some Democrats joined in demanding answers from Schapiro as to why Becker was allowed to advise on the Madoff case, including advice on how to compensate the swindler's victims.

The SEC's top watchdog has an investigation underway.

The SEC voted in 2009 on a particular method to compensate Madoff's victims, with some commissioners and staff unaware that Becker had received money from Madoff funds, sources told Reuters on Wednesday.

QUICK AND PUBLIC

Senate securities subcommittee chairman Jack Reed said after a hearing he led that there should be a thorough investigation. It should be done quickly and the response should be made public, Reed, a Democrat, told Reuters.

House and Senate Republicans are already probing the incident.

Becker's link to Madoff, his work on Madoff matters at the agency, and Schapiro's knowledge of a tie, are all raising fresh questions about the agency that missed several chances to catch Madoff before his 2008 arrest.

As the SEC struggles to implement and enforce dozens of new rules under Dodd-Frank, Schapiro said the agency will miss some deadlines for putting in place new regulations.

She told the Senate hearing that phased implementation of some rules could help avoid unintended consequences.

In 2000, the SEC's budget was about $369 million. Its budget now is $1.14 billion. It is seeking more than that for the coming fiscal year at a time when government spending is under intense pressure due to the soaring federal deficit.

Before we even think about giving this agency yet another funding increase, at minimum, the agency will need to show major progress in implementing recommended reforms to improve its operations, said Representative Scott Garrett, who chaired a Thursday morning House hearing.

BECKER'S ADVICE

Becker advised the SEC on a method to recommend for determining which victims of Madoff's Ponzi scheme should be eligible to file claims with Picard.

At first, in early 2009, the SEC took a position that would potentially hurt Becker's financial interests by recommending that investors could only file claims based on net equity, or the difference between what they put in and what they withdrew.

But later that year, the SEC changed course slightly.

People familiar with the matter say Becker was involved in advocating a change which would benefit longer-term Madoff investors by adjusting the payments to account for inflation.

That refined method was a source of internal dissent within SEC staff. When it came time to vote on it, however, there was no mention of Becker's conflict, sources said, and the SEC commissioners voted to accept the new recommendation.

The change was never put into practice, and a federal court last year upheld Picard's net equity method. Madoff victims are still fighting to get it changed.

(Reporting by Sarah N. Lynch and Kevin Drawbaugh; Editing by Tim Dobbyn)