WASHINGTON — Sales of new homes jumped 14 percent in September to the fastest pace in six months as strong demand helped offset rising prices.

The Commerce Department reported Tuesday that sales of new single-family homes rose to a seasonally adjusted annual rate of 800,000 units last month, which was well above what economists had been expecting.

However, the government revised lower its estimates for sales in the previous two months with August now showing a 1.4 percent decline to a rate of 702,000 units.

The September sales pace was the strongest since sales reached an annual rate of 873,000 in March.

The median price of a new home, the point where half the homes sold for more and half for less, rose to a record $408,800 in September, up 9.5 percent from a year ago. The average sales prices in September increased to $451,700, up 11.5 percent from a year ago.

Prices are being pushed higher by strong demand and increases being faced by builders who are grappling with shortages of critical building supplies such as lumber.

“We expect new home sales to move mostly sideways over the rest of 2021 as strong demand and low mortgage rates are tempered by high prices and construction backlogs,” said Nancy Vanden Houten of Oxford Economics.

The report showed that sales rose in all parts of the country in September except for the Midwest where they slipped 1.5 percent. Sales were up 32.3 percent in the Northeast, 17.5 percent in the South and 8.2 percent in the West.

The report on new home sales followed news last week that sales of existing homes rose to a seasonally adjusted annual rate of 6.29 million units in September, the strongest pace since January.