By Lucia Mutikani

WASHINGTON (Reuters) -U.S. single-family homebuilding rebounded in September, boosted by demand for new construction amid an acute housing shortage, but the highest mortgage rates in nearly 23 years could slow momentum and delay the overall housing market recovery.

That was flagged by other data on Wednesday showing applications for loans to purchase a home plunged last week to levels last seen in 1995. In addition, the jump in housing starts partially recouped the decline in August. The reports followed on the heels of news on Tuesday that confidence among single-family homebuilders slumped to a nine-month low in October, with builders reporting lower levels of traffic.

"Higher mortgage rates and deteriorating homebuilder sentiment will weigh on single-family starts, although the need for inventory may provide some cushion for the downside," said Nancy Vanden Houten, lead U.S. economist at Oxford Economics in New York.

Single-family housing starts, which account for the bulk of homebuilding, increased 3.2% to a seasonally adjusted annual rate of 963,000 units last month, the Commerce Department said. Data for August was revised to show starts dropping to a rate of 933,000 units instead of 941,000 units as previously reported.

Single-family starts rose in the Midwest, West and the densely populated South, but plunged 19.0% in the Northeast.

The housing market had shown signs of stabilizing before mortgage rates resumed their upward trend late in the summer, with the rate on the popular 30-year fixed mortgage breaking above 7% in August. According to the Mortgage Bankers Association, the average contract interest rate on a 30-year fixed-rate mortgage rose 3 basis points to 7.70% last week, the highest since November 2000.

Mortgage rates have risen in tandem with the yield on the benchmark 10-year Treasury note, which has spiked to a 16-year high, in part reflecting the economy's resilience.

Since March 2022, the Federal Reserve has raised its benchmark overnight interest rate by 525 basis points to the current 5.25%-5.50% range.

Starts for housing projects with five units or more soared 17.1% to a rate of 383,000 units in September. But with credit conditions tightening, builders could find it difficult to secure funding for projects. The supply of multi-family housing under construction is near record highs, which could also limit the scope for further groundbreaking on new projects.

Overall housing starts accelerated 7.0% to a rate of 1.358 million units in September. Economists polled by Reuters had forecast starts rebounding to a rate of 1.380 million units.

Permits for future construction of single-family homes rose 1.8% in September to a rate of 965,000 units, the highest since May 2022. Multi-family building permits dropped 14.0% to a rate of 459,000. Building permits as a whole declined 4.4% to a rate of 1.473 million units.

"The permits data are more of a leading indicator, but with rates pushing higher lately and homebuilder sentiment weakening, we are hesitant to get too optimistic about upcoming single-family construction activity," said Daniel Silver, an economist at JP Morgan in New York.

Residential investment has contracted for nine straight quarters, the longest such stretch since the housing market bubble burst, triggering the 2008 global financial crisis and the Great Recession.

(Reporting by Lucia Mutikani; Additional reporting by Dan Burns; Editing by Chizu Nomiyama and Andrea Ricci)