NEW YORK — Home prices tumbled by the steepest annual rate on record in the fourth quarter, two housing indexes showed today, and the pace of decline continued to gain speed in all but a handful of battered cities.

The further prices fall, the fewer homeowners may be able to qualify for President Barack Obama’s mortgage relief plan. Last week, the president estimated up to 5 million borrowers in good standing who don’t owe more than 105 percent of their home’s current value would be able to refinance into a lower interest-rate loan.

Though details of the plan won’t be released until March 4, almost 14 million homeowners are already under water, according to Moody’s Economy.com, meaning they owe more on their mortgages than their homes are worth. Nationally, home prices have receded to 2003 levels, and half the metro areas in the 20-city Standard & Poor’s/Case-Shiller Home Price Index have lost more than 20 percent of their values from their peaks in 2006, including Las Vegas, Phoenix and Miami.

“If they don’t get (the plan) into place very soon, it will be out of our reach to help these people,” said Mark Zandi, chief economist for Moody’s Economy.com.

Americans are feeling grim about the prospects of any turnaround. The consumer confidence index sank to new lows in February as huge job cuts, shrinking retirement accounts and plunging home prices fueled fears, the Conference Board said today.

The S&P/Case-Shiller index plunged 18.2 percent during the quarter from the same period a year ago, the largest drop in its 21-year history.

Meanwhile, the Federal Housing Finance Agency said today that home prices dropped 8.2 percent from a year earlier, its largest annual decline since 1991.

The reports did offer a meager amount of good news. The rate of year-over-year price declines moderated in Boston, Denver, Los Angeles, San Diego and Washington, according to the S&P/Case-Shiller index, while cities in Washington, North Dakota and Texas posted year-over-year quarterly gains, the government said.

But the Sun Belt cities continue to get clobbered. Phoenix, Las Vegas and San Francisco all saw home values lose more than 30 percent in December, the S&P/Case-Shiller index said. And the government index showed many California and Florida cities recorded their worst declines in the fourth quarter.

Prices in the S&P/Case-Shiller 20-city index have plunged 27 percent from their peak in the summer of 2006, and the 10-city index has fallen more than 28 percent. Both indices have recorded year-over-year declines for 24 straight months.

On Wednesday, the National Association of Realtors releases its existing home sales data for January. The Commerce Department releases its new home sales figures for January on Thursday.