Nearly 10 million U.S. households remain stuck in homes worth less than their mortgage and a similar number have so little equity they can't meet the expenses of selling a home, trends that help explain recent sluggishness in the housing recovery.

At the end of the first quarter, some 18.8% of U.S. homeowners with a mortgage—9.7 million households—were "underwater" on their mortgage, according to a report scheduled for release Tuesday by real-estate information site Zillow Inc. While that is an improvement from 19.4% at the end of last year and a peak of 31.4% 2012, those figures understate the problem.

In addition to the homeowners who are underwater, roughly 10 million households have 20% or less equity in their homes, which makes it difficult for them to sell their homes without dipping into their savings. Most move-up homeowners typically use their home equity to cover broker fees, closing costs and a down payment for their next home. Without those funds, many homeowners can't sell.

"It's a sobering appreciation that negative equity is going to be with us for a while to come," said Stan Humphries, Zillow's chief economist. "Negative equity is central to understanding a lot of the distortions in the marketplace right now."

Those distortions include the inventory of homes for sale, which, while rising, is low by historical standards. It also helps explain why first-time home buyers are having such a hard time cracking the market. Real estate is in some ways like a ladder, Mr. Humphries notes, so when underwater homeowners don't trade up it makes it harder for newcomers to get in.