By Lauren Tara LaCapra

NEW YORK, Nov 12 (Reuters) - Goldman Sachs Group Inc Chief Executive Lloyd Blankfein said on Tuesday that he regrets collateralized debt obligation trades the Wall Street bank made in the run-up to the financial crisis that later caused a firestorm of public criticism.

Collateralized debt obligations (CDOs) are pools of bonds that are bundled, sliced up according to credit risk, and sold to investors. As the mortgage market heated up leading into 2007, investment banks began selling more exotic varieties linked to mortgages.

Wrong-way bets on CDOs led to billions of dollars' in losses for many investors and some investment banks, including Merrill Lynch. But unlike its Wall Street peers, Goldman Sachs profited by using CDOs to bet that the mortgage market would collapse.

While the trades were profitable at the time - to the tune of $13 billion, according to a congressional committee - Goldman suffered tremendous reputational fallout in the years after the crisis.

"I wish the organization hadn't done complex CDOs circa '06 and '07," Blankfein said at an industry conference in New York.

"And, post-crisis, I wish I had gotten off - a little quicker off the mark in describing who we were and what we did as a firm and how we looked to the world before everybody defined us for us," he continued. "We were competing against an existing narrative - it's very hard to get out of (that)."

The SEC brought civil fraud charges against Goldman in 2010 related to a CDO called "Abacus," arguing that the bank defrauded clients who took long positions.

Goldman settled for $550 million without admitting to or denying wrongdoing, but the reputational damage it suffered from that lawsuit - as well as a damning congressional report - has taken years to repair.

On stage at the conference, hosted by the industry trade group SIFMA, Blankfein said Goldman's work is not yet done.

In response to a question about JPMorgan Chase & Co's recent legal and regulatory challenges, Blankfein said that although senior Goldman executives are back to spending the majority of their time dealing with ordinary business issues, they still have to worry about the consequences of actions the firm took years ago.

"You say the spotlight's off - it's not completely off," Blankfein said. "We're still dealing with legacy issues."