Elevated mortgage rates, along with fast-rising home prices, have cast a chill over the U.S. housing market because they are forcing prospective buyers to budget hundreds of extra dollars, or more, in monthly costs. The rise in rates also has choked off refinancing business, putting some mortgage companies in dire straits.

For much of the past decade, mortgage rates have hovered near record lows, fueling brisk demand in the housing market. But rates have jumped this year as a result of the Federal Reserve’s decision to lift interest rates.

The central bank has indicated it will continue to lift rates to fight inflation, meaning mortgage rates will likely remain high for some time. The 30-year mortgage rate tends to track the yield on the benchmark 10-year Treasury note, which has roughly doubled this year.

The housing market is a focal point in the Fed’s effort to curb inflation, since shelter costs have been a significant contributor to the rise in living expenses. Skyrocketing rents and home costs have made it even tougher for many Americans to find affordable housing.

The minutes from the Fed’s policy meeting last month, released Wednesday, noted that “housing activity had weakened notably, reflecting the impact of higher mortgage interest rates and house prices on home affordability.”

Write to Ben Eisen at ben.eisen@wsj.com