By Lucia Mutikani

WASHINGTON (Reuters) - U.S. homebuilding rose to a nine-month high in December amid a surge in multi-family housing projects, but soaring prices for materials after the government nearly doubled duties on imported Canadian softwood lumber could hamper activity later this year.

The report from the Commerce Department on Wednesday also showed the housing construction backlog surged to a record high last month, underscoring the challenges builders are facing from supply strains, including labor shortages. Completions tumbled as well. Rising mortgage rates could also restrain homebuilding.

"Builders are gladly trying to meet demand, but supply problems and labor shortages are slowing them down," said Jennifer Lee, a senior economist at BMO Capital Markets in Toronto. "Softwood lumber duties are going to hurt this spring."

Housing starts rose 1.4% to a seasonally adjusted annual rate of 1.702 million units last month, the highest level since March. Economists polled by Reuters had forecast starts falling to a rate of 1.650 million units.

The volatile multi-family housing segment accounted for the rise in homebuilding last month, with starts for buildings with five units or more surging 13.7% to a rate of 524,000 units. There is strong demand to rental housing.

Single-family housing starts, which account for the largest share of the housing market, dropped 2.3% to a rate of 1.172 million units last month. Single-family homebuilding soared in the Northeast and Midwest, likely boosted by unseasonably mild temperatures. December 2021 was the warmest December on record, according to the National Centers for Environmental Information.

The densely populated South, where the bulk of homebuilding occurs, reported an 8.2% decrease in single-family starts. Homebuilding also fell in the West.

Housing starts totaled 1.595 million in 2021, up 15.6% from 2020. But the outlook for home building this year is uncertain. The United States last November nearly doubled the duties on imported Canadian softwood lumber to 17.9% from 9% after a review of its anti-dumping and countervailing duty orders.

According to the National Association of Homebuilders on Tuesday, the aggregate cost of residential construction materials had increased almost 19% since December 2021. The NAHB said higher material costs and shortages were adding weeks to typical single-family home construction times.

Prices for softwood lumber, used for framing, soared 24.4% in December after rising 6.9% in November, according to the latest producer price data. Lumber futures have also surged.

Stocks on Wall Street were lower. The dollar slipped against a basket of currencies. U.S. Treasury prices rose.

HUGE BACKLOG

The backlog of houses authorized for construction but not yet started shot up 1.1% to a rate of 270,000 last month, the highest on record. Permits for future homebuilding jumped 9.1% to a rate of 1.873 million units in December, an 11-month high. They accelerated 17.2% in 2021.

Permits are now running ahead of starts, which should underpin homebuilding in the coming months. Permits for buildings with five units or more soared 19.9% to a rate of 675,000 units. Single-family building permits rose 2.0% to a rate of 1.128 million units.

An acute shortage of previously owned homes available for sale is supporting homebuilding, but rising mortgage rates, supply constraints together with higher house prices could make home purchasing less affordable.

Housing completions tumbled 8.7% to a rate of 1.295 million units, reflecting a 34.3% plunge in multi-family housing units. Single-family home completions increased 3.9% to a rate of 990,000 units.

The inventory of single-family housing under construction rose 2.3% to a rate of 769,000 units last month, the highest since February 2007. Multi-family homes under construction advanced 2.4% to a rate of 737,000 units.

"As long as supply chains remain stressed, builders will struggle to complete projects, slowing sales and likely limiting growth in the supply of new homes," said Ben Ayers, senior economist at Nationwide in Columbus, Ohio.

The 30-year fixed-rate mortgage averaged 3.45% during the week ending Jan. 13, the highest since March 2020 and up from 3.22% in the prior week, according to data from mortgage finance agency Freddie Mac.

An analysis by another mortgage finance agency Fannie Mae on Wednesday showed housing affordability was increasingly becoming constrained, which could limit home sales this year.

"We observe an early indication of this in recent increases in debt-to-income measures associated with incoming mortgage originations," said Doug Duncan, chief economist at Fannie Mae in Washington.

Mortgage rates have risen as financial markets price in an interest rate increase from the Federal Reserve in March amid high inflation and a labor market that is at or near maximum employment.

Expectations that mortgage rates will keep rising are drawing buyers into the market.

A report from the Mortgage Bankers Association on Wednesday showed applications for loans to buy a home increased 8% last week.

"This year is likely to be sideways at best for residential home builders," said Christopher Rupkey, chief economist at FWDBONDS in New York. "It will be interesting to see if higher mortgage rates cool the housing bubble in prices because the lack of new supply will likely remain the dominant trend for another year."

(Reporting by Lucia Mutikani; Editing by Chizu Nomiyama and Andrea Ricci)