WASHINGTON, May 5 (Reuters) - Sales of new U.S. single-family homes increased in February and March as the drag from harsh weather faded, but higher mortgage rates because of the impact of the war with Iran could limit further gains.

New home sales surged 7.4% to a seasonally adjusted annualized rate of 682,000 units in March, the Commerce Department's Census Bureau said on Tuesday. Sales increased to a rate of 635,000 units in February from 583,000 units in January, when they were weighed down by winter storms.

The Census Bureau has caught up on releasing the new home sales data following delays caused by last year's government shutdown. New home sales account for a small share of U.S. home sales and tend to be volatile on a month-to-month basis.

New home sales are counted at the signing of a contract. They rose 3.3% on a year-over-year basis in March. The average rate on the popular 30-year fixed-rate mortgage jumped from 5.98% in late February to 6.46% at the start of April, data from Freddie Mac showed. It averaged 6.30% last week.

Despite the strong sales in March and February, new housing inventory remained high. An oversupply of new homes on the market is one of the factors deterring builders from aggressively breaking ground on new single-family housing projects. There is a dearth of previously owned properties for sale, especially starter homes.

New housing inventory dipped to 481,000 units in March from 483,000 units in February. At March's sales pace, it would take 8.5 months to clear the supply of new houses on the market, down from 9.1 months in February.

With supply still elevated, the median new house price dropped 6.2% to $387,400 in March from a year earlier. Most of the homes sold in March were under $399,999.