Washington ? The Federal Reserve offered super-low interest rates for two more years Tuesday — an unprecedented step to arrest an economic free fall that dragged down the stock market. Wall Street roared its approval and finished a wild day with a 429-point gain.

The rally was remarkably fast — the Dow Jones industrial average was still down for the day with less than an hour of trading to go — and enough to erase two-thirds of its decline the day before.

The Fed set its target for interest rates near zero in 2008 as a response to the financial crisis that fall. Since then, it had said only that rates would stay low for an “extended period.” On Tuesday, it said that would be at least through mid-2013.

But the Fed also said it expects the economy to stay weak for two more years, longer than the Fed had previously indicated. It has already been more than two years since the end of the Great Recession.

The central bank left open the possibility of a third round of bond purchases designed to hold interest rates down and push stock prices up. The second round, announced last year, sparked a 28 percent rally in the Dow through April 29.

It was an unusually volatile day of trading. The Dow was up about 200 points most of the morning. It was up about 100 when the Fed statement came out at 2:15 p.m. Within half an hour, the Dow was down more than 200.

But investors warmed to the Fed news, and the Dow made a bumpy, steep climb for the final stretch of trading. That included a 640-point swing from its lowest point of the day to its highest.

The Dow closed at 11,239.77, up 4 percent. The S&P 500 finished up 4.7 percent and the Nasdaq composite index up 5.3 percent.

The yield on the 10-year Treasury bond briefly hit a record low, 2.03 percent, and finished at 2.26 percent. Investors have bought U.S. debt, driving yields down, even after S&P stripped the United States of its top-of-the-line credit rating last week.

Interest rates on consumer loans, including adjustable-rate mortgages, car loans and credit cards, are often based on Treasury rates. So mortgage rates, which are already among the lowest ever, could go even lower.

Low interest rates for two more years could make the stock market a better bet because bonds will return less money. That appeared to be at least part of the reason stocks rallied so much after investors had a chance to digest the Fed’s statement.

Some analysts also attributed the late-day rally to wording in the Fed’s statement suggesting it might take further steps to stimulate the economy in the future.

The stock rally came after two and a half weeks of almost uninterrupted declines. Those were fueled first by uncertainty about the federal debt ceiling, then by concerns that the U.S. economy is headed for a new recession and about out-of-control European debt.

When it came late Friday, the downgrade only added anxiety. On Monday, the first day of trading after it was announced, the Dow fell 634 points. Even counting Tuesday’s gains, the Dow is down 11.6 percent since July 21 — almost 1,500 points.

The Fed’s announcement of a two-year timeframe for any rate increase underscored a stark reality: A sluggish economy and painfully high unemployment have become chronic.