How much good will can an apology  and half a billion dollars  buy? A lot, Goldman Sachs is hoping.

After first staunchly defending its outsize profits and pay, and then bristling at calls for restraint in these tough economic times, Goldman is trying a new tack: It is apologizing for past mistakes that led to the financial crisis  and sharing at least some of its riches.

A little more than a week after Goldman’s chairman and chief executive drew fire for saying the Wall Street giant was “doing God’s work,” the bank said Tuesday that it would spend $500 million  or about 3 percent of the $16.7 billion it has so far set aside to pay its employees this year  to help thousands of small businesses recover from the recession.

At the same time, the executive, Lloyd C. Blankfein, also showed a bit of humility, acknowledging at a conference in New York that Goldman had made mistakes, and that it was sorry. “We participated in things that were clearly wrong and we have reasons to regret and apologize for,” he said.