Condo prices in Boston hit fresh highs last year, thanks to sales at several new high-end buildings and the continuing demand for living in the core of the city.

The median price of a condo in central Boston — neighborhoods from the Fenway to downtown to South Boston — jumped 16.2 percent last year, to $790,000, according to the real estate data firm LINK. The median price for a unit in a high-end, full-service building climbed almost twice that fast, to more than $2 million.

The luxury market was driven, in part, by a few big new buildings, such as Millennium Tower, which opened last year downtown. Millennium’s Grand Penthouse is now home to the globe-hopping private equity billionaire Jonathan Grayken, who spent $35 million on the place in August.

The broader market is being powered by a combination of young professionals, suburban empty-nesters, and some international buyers, all of whom are drawn to Boston’s growing job base and urban life, said LINK’s president, Debra Taylor Blair.

She noted that prices on very small units — 450 square feet or less — are climbing especially fast, because younger and first-time buyers want to live close to their jobs. Sales were also strong in many older luxury buildings. Both, she said, are signs of solid demand across the whole market.

“It’s not just the rich getting richer,’’ Taylor Blair said. “This is a tide that’s rising across the board.’’

But a wave of new units could test the strength of the city’s condo market in the next few years. To date, much of the housing built in the city during the current boom has been apartments, enough to cause rents at the high end of the market to plateau.

Data released in early January showed that apartment rental prices fell slightly at the end of 2016 — the first drop since 2010 — amid a surge of new buildings that have opened in Boston and neighboring cities such as Cambridge, Chelsea, and Somerville.

The decline was modest, just 1.7 percent — or $36 a month on the average lease of $2,038, according to the rental-tracking firm Reis Inc. But it was the latest and clearest sign that the flood of construction in Boston is putting a lid on rents, at least at the upper end of the market.

Yet in central Boston, buyers are finding that condo prices are climbing much faster than prices for single-family homes, or the market generally.

And now the apartment-condo mix is changing.

Thousands of new condominium units are set to open this year and next, from stand-out towers such as One Dalton in the Back Bay and the Pierce in the Fenway, to more modest buildings in South Boston and the South End.

Thousands more are planned or already being built, including Cottonwood Management Group’s so-called M Block project in the Seaport, where more than half of the 733 units will be condos.

Taylor Blair has heard some fears that there could soon be a glut. But, she said, the steady price growth, along with a historically fast pace of sales, suggest a lot of customers are still looking to buy.

“Oversupply is the big fear,’’ she said. “But what these numbers say to us is that there’s a lot of pent-up demand out there to live in Boston.’’

And Boston’s residential real estate market is often seen as one with little downside risk. Standard & Poors, for example, recently estimated that if another recession hits — even one of the magnitude of the economic downturn that began in 2007 — Boston-area home prices would dip less than 2 percent.

Even under the worst-case scenario envisioned by S&P, values in Greater Boston would slip 6 percent, compared to a 27 percent plunge nationally.

Tim Logan can be reached at tim.logan@globe.com. Follow him on Twitter at @bytimlogan.