WASHINGTON — Sales of existing homes rose by the largest amount in more than five years in September, a real estate trade group said. The data is a possible glimmer of hope that the housing slump could be starting to bottom out.

The National Association of Realtors said Friday that sales of existing homes rose by 5.5 percent in September compared to August, the best showing since a 5.6 percent increase in July 2003, during the five-year housing boom.

Even with the gain in sales, prices kept falling. The median sales price has dropped to $191,600, down by 9 percent from a year ago.

Inventories of unsold existing homes dropped by 1.6 percent in September to 4.27 million units which would be a 9.9 months supply at the September sales pace, still a historically high level.

Lawrence Yun, chief economist for the Realtors, said a sales turnaround first seen in California was beginning to broaden to other regions of the country. He said housing may be starting to find a bottom but the turnaround could be aborted by the near-certainty that the country has fallen into a recession. For that reason, he said it was important for Congress to pass a second stimulus package including measures that would bolster the housing market.

In a further effort to bolster the market and deal with record high levels of mortgage defaults, Shelia Bair, the head of the Federal Deposit Insurance Corp., is pushing Treasury to include in the $700 billion rescue package for the financial system a new program to prevent more foreclosures.