LOS ANGELES — Sales of previously occupied U.S. homes fell last month to the slowest pace since January, as elevated mortgage rates and a stubbornly low inventory of homes on the market combined to discourage many would-be homebuyers.

Existing home sales fell 2.2% last month from June to a seasonally adjusted annual rate of 4.07 million, the National Association of Realtors said today. That’s below the 4.15 million pace that economists were expecting, according to FactSet.

Sales slumped 16.6% compared with July last year. It was also the lowest home sales pace for July since 2010.

The national median sales price rose 1.9% from July last year to $406,700, marking the first annual increase in prices since January. Roughly 35% of homes sold in July fetched more than their list price, said Lawrence Yun, the NAR’s chief economist.

“At least when it comes to home prices, it looks like the housing recession is already over,” Yun said.

The shortage of homes for sale has kept the market competitive, driving bidding wars in many places, especially for the most affordable homes.

All told, there were 1.11 million homes on the market by the end of last month, down 14.6% from a year earlier, the NAR said.

“There’s virtually no inventory at the lower price point,” Yun said.

The latest housing market figures are more evidence that many house hunters are being held back by a persistently low inventory of homes for sale and rising mortgage rates.

The average rate on a 30-year home loan hovered just below 7% last month and has continued climbing, reaching 7.09% last week, according to mortgage buyer Freddie Mac. The average long-term U.S. mortgage rate is now at its highest level in more than 20 years.

High rates can add hundreds of dollars a month in costs for borrowers, limiting how much they can afford in a market already unaffordable to many Americans. They also discourage homeowners who locked in those low rates two years ago from selling.