Stocks were little changed immediately after the Fed announcement, but later rose sharply amid growing investor optimism that the economy was indeed rebounding.

"The Fed delivered as expected," said Chris Wolfe, equity market strategist for JP. Morgan Private Bank. "Stock markets have rallied since the low point in March, and you have a lot of good news built in. The equity markets basically didn’t want a surprise."

"In the meantime, you’ve got a Fed that continues to be accommodative, and you’ve got corporations continuing to do the right thing, although it may take a long time to see a lot of hiring," he said. "That will keep pressure on the Fed to keep rates low."

The Dow Jones industrial average closed up 92.71, or 1 percent, at 9,310.06, following a five-day gain of 273 points.

The broader market also rose. The Nasdaq composite index advanced 25.50, or 1.5 percent, to 1,687.01. The Standard & Poor’s 500 index gained 9.76, or 1 percent, to 990.35.

The Fed unanimously voted to keep the federal funds rate at 1 percent today. In its decision, policymakers said the risk of deflation, although remote, continues to exceed that of inflation. That allayed investor fears that rates would be raised in the near future.

"Investors want(ed) the Fed to say the economy is improving but not so much that rates will be increasing at any time in the future," said Richard J. Nash, chief market strategist at Victory Capital Management.

Trading has been erratic in recent weeks as investors, having sent the market surging since mid-March, worried that the rally might have come too fast. They now want to see stronger evidence of a solid recovery, particularly when several economic reports are released later this week.

"It’s a busy week on the calendar with retail sales and consumer confidence being the most important numbers," Nash said. "Folks are going to be following the economic data to see if the (market) jump we had in June and July will be sustainable going forward."

Deere gained $2.53 to $53.51 after the manufacturer posted earnings that beat Wall Street’s estimates, citing better sales of nonagricultural equipment.

Clorox rose $1.05 to $43.87 after the maker of bleach and Kingsford Charcoal reported fiscal fourth-quarter profit that met analysts’ estimates as well as its own lowered forecasts.

Marvel Enterprises climbed $2.85 to $21.50 after the comic book publisher reported quarterly earnings that beat expectations; it also raised its third-quarter outlook.

Decliners included J.C. Penney, which fell 31 cents to $17.76, after the retailer posted a narrower second-quarter loss, citing higher sales at its department store division.