Thanks to rising home prices, about 312,000 residential properties returned to positive equity in the first quarter, but 6.3 million others, or 12.7% of all properties with a mortgage, were still in negative equity, according to CoreLogic.

The national aggregate value of negative equity was $383.7 billion at the end of the first quarter, down $16.9 billion from approximately $400 billion in the fourth quarter of 2013.

Of the 43 million residential properties with equity, approximately 10 million have less than 20% equity and thus are considered “under-equitied.” These homeowners may have a more difficult time refinancing due to underwriting constraints. Under-equitied mortgages accounted for 20.6% of all residential properties with a mortgage in the first quarter, according to CoreLogic.

About another 1.5 million properties have less than 5% equity, referred to as near-negative equity. These homeowners are at risk of going back underwater if home prices fall.

"Despite the massive improvement in prices and reduction in negative equity over the last few years, many borrowers still lack sufficient equity to move and purchase a home," says Sam Khater, deputy chief economist for CoreLogic, in a release. "One in five borrowers have less than 10 percent equity in their property, which is not enough to cover the down payment and additional costs associated with a conventional mortgage."

"Prices continue to rise across most of the country and significantly fewer borrowers are underwater today compared to last year," adds Anand Nallathambi, president and CEO of CoreLogic. "An additional rise in home prices of 5 percent, which we are projecting will occur over the next 12 months, will lift another 1.2 million properties out of the negative equity trap."