New-home sales rose in May and prices hit a record level, more evidence of a housing market characterized by strong demand and tight inventories.

Purchases of new, single-family homes—a narrow slice of all U.S. home sales—rose 2.9% to a seasonally adjusted annual rate of 610,000 in May, the Commerce Department said Friday.

From a year earlier, new-home sales rose 8.9% in May and so far this year have climbed 12.2%, indicating the market for new homes appears to be picking up.

“The name of the housing market game over the past few years has been low supply, not low demand,” said Ralph McLaughlin, chief economist at Trulia. “As home sales continue to pick up, that’s further evidence that we have a supply problem, not a demand problem.”

The median sale price for a new home sold in May was $345,800, the highest recorded for data dating back to 1963. The average sale price also came in the highest on record at $406,400. Home prices for new homes have climbed steeply since dipping during the recession.


“It’s going to be very hard to sustain price increases of any large amount going forward because they are pushing against people’s ability to afford homes,” said Brad Hunter, chief economist at HomeAdvisor.

Several factors are converging to help strengthen buyer demand. The national unemployment rate in May was 4.3%, a 16-year low, and the economy continued to expand and add jobs in the first half of 2017.

Still, the slow pace of new construction is constraining supply. Housing starts declined for the third straight month in May, as builders expressed concern about tight availability of lots and a labor shortage.

At the current sales pace, there was a 5.3 months’ supply of new homes on the market in May, a relatively low level.


“Ultimately this report is a disappointment for those looking to builders to meaningfully help solve the pressing supply issues in the market overall, especially for entry-level buyers,” said Svenja Gudell, chief economist at Zillow.

Earlier this week, the National Association of Realtors reported sales of existing homes, which make up the bulk of the market, rose 1.1% in May to a seasonally adjusted annual rate of 5.62 million. The median property remained on the market just 27 days in May, the shortest time since the trade group began tracking the metric six years ago.

“The pressure to close deals quickly, which has afflicted the existing home sales market, is also seeping into the market for new homes,” Ms. Gudell said.

New homes that weren’t started but already sold reached 208,000, the highest level since May 2007.


Write to Sarah Chaney at sarah.chaney@wsj.com and Jeffrey Sparshott at jeffrey.sparshott@wsj.com