Price growth for previously owned homes, which make up most of the housing market, slowed in the fourth quarter from earlier in the year but remained unusually strong due to robust demand and a shortage of homes for sale.

The median sales price for single-family existing homes was higher in the quarter compared with a year ago for 181 of the 183 metro areas tracked by the National Association of Realtors, the association said Thursday.

In the fourth quarter, the typical monthly mortgage payment for a single-family home rose to $1,240, from $1,039 a year earlier, NAR said.

“Home buyers in the last quarter saw little relief as home prices continued to climb, albeit not as fast as earlier in the year,” said

Lawrence Yun,

NAR’s chief economist. “A number of families, especially would-be first-time buyers, are increasingly being forced out of the market.”

Median prices rose by more than 10% from a year earlier in 67% of the 183 metro areas, a slowdown from the third quarter when 78% of metro areas reported double-digit-percentage growth.

Nationwide, the median single-family existing-home sales price rose 14.6% in the fourth quarter from a year ago to $361,700, NAR said. That is a slight decline from the record median sales price of $363,100 reached in the prior quarter.

Mortgage-interest rates have continued to rise this year. The average rate on a 30-year fixed-rate mortgage was 3.69% as of Thursday, said mortgage-finance company

Freddie Mac,

the highest level since January 2020.

Mortgage lenders began adjusting their rates upward after the Federal Reserve said it would wind down its purchases of close to $2.7 trillion in mortgage-backed securities it had amassed during the pandemic. When demand for mortgage bonds falls, issuers must offer higher yields to entice investors. That requires lenders to charge borrowers higher interest rates.

High inflation readings are making investors more certain that the central bank will raise its short-term rate in an effort to control prices. Mortgage rates are closely tied to the yield on the benchmark 10-year Treasury, which reached 2% Thursday for the first time since 2019.

The acceleration of mortgage rates will likely have an “adverse impact on homebuyer demand,” said

Sam Khater,

Freddie Mac’s chief economist.

In recent weeks, home shoppers have been eager to buy before interest rates rise further, real-estate agents say. Active listings in the four weeks ended Jan. 30 fell 29% from a year earlier, according to real-estate brokerage

Redfin Corp.

The ability for some households to work remotely continues to spur home-buying demand. Millions of millennials are also aging into their prime home-buying years.

The Punta Gorda, Fla., metro area posted the strongest median-price increase in the fourth quarter, up 28.7% from a year earlier.

Following Punta Gorda was the Ocala, Fla., metro area, up 28.2%, and Austin, Texas, up 25.8%.

The only metro areas to post a decline in the fourth quarter from a year earlier were Davenport, Iowa, where median prices fell 1.1%, and Peoria, Ill., down 0.1%, NAR said.

News Corp,

owner of The Wall Street Journal, also operates Realtor.com under license from NAR.

—Orla McCaffrey contributed to this article.

Write to Nicole Friedman at nicole.friedman@wsj.com