WASHINGTON (Reuters) - U.S. single-family homebuilding increased solidly in December, but further gains were seen limited by rising mortgage rates and a glut of new homes on the market.

Single-family housing starts, which account for the bulk of homebuilding, rose 3.3% to a seasonally adjusted annual rate of 1.050 million units last month, the Commerce Department's Census Bureau said on Friday. Data for November was revised higher to show homebuilding increasing to a rate of 1.016 million units from the previously reported pace of 1.011 million units.

Higher mortgage rates have weighed on homebuilding, which had been benefiting from a dearth of previously owned houses for sale. Mortgage rates have risen in tandem with U.S. Treasury yields, which have surged on economic resilience and investor worries that President-elect Donald Trump's proposed policies, including tax cuts, higher tariffs on imported goods and mass deportations, could fan inflation.

The Federal Reserve has lowered its projected interest rate cuts for this year to only two from the four it estimated in September when it commenced its policy easing cycle. The U.S. central bank has reduced its benchmark overnight interest rate by 100 basis points to the 4.25%-4.50% range. The policy rate was hiked by 5.25 percentage points in 2022 and 2023.

The average rate on the 30-year fixed-rate mortgage rose above 7% this week for the first time since May, mortgage finance agency Freddie Mac said on Thursday.

Homebuilders cheered Trump's victory in the Nov. 5 election amid hopes for a less stringent regulatory environment. However, economists have warned of higher prices for building materials and worker shortages at construction sites if the new administration proceeds with its immigration and trade policies.

The National Association of Home Builders/Wells Fargo housing market index was unchanged in January after rising in the prior two months, with builders complaining about high borrowing and construction costs.

There is an oversupply of unsold new homes, with inventory at levels last seen in late 2007.

Permits for future construction of single-family housing increased 1.6% to a rate of 992,000 units in December.

"The elevated level of inventory of unsold new homes on builders' books suggests that any eventual upturn in demand, as and when mortgage rates eventually fall, will feed through only weakly to building activity," said Samuel Tombs, chief U.S. economist at Pantheon Macroeconomics.