The national negative equity rate ended 2013 below 20 percent for the first time in years, while Boston’s negative equity rate dipped to nearly 10 percent, according to a new report from real estate portal Zillow.

Across the country, 19.4 percent of all homeowners with a mortgage remain underwater, down from 27.5 percent in the fourth quarter of 2012. More than 3.9 million homeowners returned to positive equity in 2013, leaving approximately 9.8 million still underwater across the country.

In Boston, those numbers were even better, with 10.4 percent of homeowners underwater, down from 16.9 percent in the fourth quarter of 2012. Negative equity in the Boston metro area peaked at 22 percent in the first quarter of 2012.

The report cautioned, however, that the "effective" negative equity rate, which includes those homeowners with a mortgage with 20 percent or less equity in their homes, remains stubbornly high. More than one-third of homeowners with a mortgage (37.6 percent) are effectively underwater, unable to sell their homes for enough profit to comfortably meet expenses related to listing a home and purchasing a new one.

"We’ve reached an important milestone as negative equity has fallen below 20 percent nationwide, which has helped free up marginally more inventory and contribute to further stabilization of the market," Zillow Chief Economist Stan Humphries said in a statement. "But a number of headwinds will prevent negative equity from falling at the kind of sustained, rapid pace we need before the market can completely return to normal, and it remains roughly four times what it is in a healthier market. High negative equity is just another sign of how distorted the market continues to be, and how far we still have to go on the road back to normal."

Home values ended 2013 up 6.6 percent, the single-largest contributor to the falling negative equity rate. But the pace of home value appreciation is slowing, with home values expected to rise just 3.4 percent over the next 12 months, according to the most recent Zillow Home Value Forecast. In Boston, Zillow projects prices will rise 2.1 percent over the coming year. As home value appreciation slows, the pace of negative equity improvement will slow.

Nationwide, Zillow predicts that the negative equity rate is will fall to 17.2 percent by the end of 2014. Negative equity is expected to rise in 26 metro markets nationwide, and remain flat in another 227 metros.

In greater Boston, Plymouth County is the most underwater, with 15 percent of homeowners with mortgages in negative equity.  In Essex Country, 11.7 percent of homeowners with a mortgage are underwater; in Middlesex Country, 7.7 percent, in Norfolk County 9.5 percent and in Suffolk Country 12 percent.