WASHINGTON U.S. single-family homebuilding surged in July amid an acute shortage of previously owned houses, but mortgage rates climbing back to near two-decade highs could stifle demand for new construction.

Single-family housing starts, which account for the bulk of homebuilding, jumped 6.7% to a seasonally adjusted annual rate of 983,000 units last month, the Commerce Department said on Wednesday. Data for June was revised to show starts falling to a rate of 921,000 units, instead of 935,000 units as previously reported.

The housing market, pummeled by the Federal Reserve's aggressive monetary policy tightening, had in recent months shown signs of stabilizing at a lower level, with homebuilding and new home sales even rising.

But further improvement looks likely to be curtailed by the renewed increase in mortgage rates.

The average rate on the popular 30-year fixed mortgage has increased to 6.96% over the past weeks, according to data from mortgage finance agency Freddie Mac. The rate is within striking distance of the 7.08% seen in late October and early November, which was the highest since April 2002.

Mortgage rates near 7% were attributed to the ebb in confidence among homebuilders in August, with the National Association of Home Builders noting that more builders were offering incentives to attract buyers amid expectations of lower sales.

Starts for housing projects with five units or more were unchanged at a rate of 460,000 units in July. Demand for rental accommodation, largely driven by higher mortgage rates sidelining some potential home buyers, is slowing. There is also a huge stock of multi-family housing under construction.

Overall housing starts increased 3.9% to a rate of 1.452 million units in July. Economists polled by Reuters had forecast starts rising to a rate of 1.448 million units.

Permits for future construction of single-family homes rose 0.6% in July to a rate of 930,000 units.

(Reporting By Lucia Mutikani; Editing by Chizu Nomiyama)