CORRECTION: An earlier version of this story incorrectly termed the drop in negative equity at the national and state levels as a drop in foreclosures. The CoreLogic report contains data on the change in negative equity, not foreclosures.

The number of borrowers who owe more than their homes are worth fell again during the first quarter, another sign of a rebounding housing market that is enjoying surging home prices, according to a report released Wednesday.

Only 9.7 million borrowers were underwater on their mortgage in the first quarter, or nearly 20 percent of mortgage holders, down from 11.4 million properties, or 23.7 percent of homes during the same period last year, according to research firm CoreLogic.

While areas hardest hit by the housing crisis — including Nevada, Florida and Arizona — saw the number of underwater borrowers decline, they are still well above the national average. More than 45 percent of homes were underwater in Nevada in the first quarter, the highest in the country.

The market also improved in the Washington area where home prices are rising at a fast pace. About 22 percent of borrowers were still underwater during the first quarter, compared with 23.5 percent last quarter and 26.6 percent a year ago.

The percentage of underwater borrowers fell the most in Virginia. Only 17 percent of borrowers there are underwater, compared with 22.3 percent during the same period last year. It was highest in Maryland where 22.6 percent of borrowers were underwater, a slight improvement from 24.7 percent last year.

In the District, the percent of underwater borrowers fell to 9.7 percent in the first quarter, compared with 12.7 percent during the same period last year.

The housing market has been experiencing a significant rebound, held back only by a lack of housing inventory. Low mortgage rates and a healthier economy have drawn out more buyers and helped home prices rise 10.9 percent nationally in March, the fastest rate in seven years, according to the Standard & Poor’s Case-Shiller index.

That has allowed underwater borrowers to regain ground. But not all those who are above water are in a position to sell — and that is keeping the housing inventory below normal levels.

More than 11 million homeowners have less than 20 percent equity on their homes, and at least 2 million of them have less than 5 percent, according to CoreLogic. Some of those borrowers could find themselves underwater again if the housing market stumbles.

That also makes those borrowers reluctant to sell. When prices rise further, these homeowners should be more confident about selling, which will help ease some of the pressure on the housing inventory, said Mark Fleming, chief economist at CoreLogic.

“You can’t sell if you don’t have the equity in your home to pay the down payment for the next one,” Fleming said.

The report found that homes priced above $200,000 are more likely to have equity. Nearly 90 percent of homes priced above $200,000 have equity while only 73 percent of homes below that price do.