Twin Cities homebuilders are having their best year in nearly a decade amid strong demand for rental apartments and dwindling supplies of new and existing houses.

Residential builders were issued 5,339 permits to build 10,303 housing units throughout the 13-county metro this year, a 14-percent increase in units and the most since 2006, according to a year-end report from the Builders Association of the Twin Cities.

“I had a good year, it was a breath of fresh air,” said Curt Christensen of Lee Lyn Construction in Watertown, who said that sales of custom homes at his company were up about 60 percent this year. “It was nice to be back at work and to be able to build a little profit back into the job.”

The industry has gotten a boost from declines in the unemployment rate, enabling more people to buy their own place or trade up to a bigger one, marking the second year of recovery for builders.

In particular, there’s been a strong increase in demand for new apartments and other kinds of multifamily housing, which represented about half of the total permitted units. In the Twin Cities, the rental boom has been concentrated in Minneapolis and St. Paul, and in inner-ring suburbs that offer the best proximity to transportation and jobs.

The big comeback story of the year for builders, however, was a strong and persistent increase in new home sales, which increased 26 percent compared with 2012.

“We enjoyed a very good 2013,” said Hans Hagen, a longtime builder in the Twin Cities. “Homebuyers also took advantage of low interest rates to purchase larger homes with more features.”

Hagen said sales at his company were up 26 percent this year compared with 2012, and that his backlog of houses scheduled for delivery in 2014 is up more than 35 percent. Construction activity is expected to increase at least through the first two quarters of 2014, he said.

Much of that demand has been fueled by a shortage of homes for sale, forcing buyers who can’t find an existing home to build one. Inventory levels are near record lows in the Twin Cities and beyond as homeowners wait for higher home prices before putting their home on the market.

Economists with Wells Fargo Securities said the inventory of new homes for sale also remains extremely low, falling 6.7 percent in November to just a 4.3-month supply. And on Tuesday, the U.S. Commerce Department said that new home sales across the country fell 2.1 percent in November, but that a sizable upward ­revision to previous months’ data suggested that the housing recovery remains well in place.

While topping the 10,000 mark for new units is indeed a milestone for Twin Cities builders, construction activity is still far below a peak of several years ago when more than 18,000 houses and apartments were built in the region.

“Ten thousand units is a nice benchmark,” said Wendy Danks, the Builders Association’s director of marketing, “but 12,000 to 15,000 is where we need to be.”

Assuming that household growth continues and interest rates remain relatively low, analysts at Wells Fargo expect new home sales to post another healthy increase nationally, rising to a pace of about 530,000 units next year.

Christensen, the custom homebuilder, agrees. He said that even at a time when sales are typically slow, he’s working with three buyers.

“That’s a rarity going through the holidays,” he said. “I think buyers are finally getting the comfort level to pull the trigger.”