A powerful combination of low mortgage rates, high demand, and few choices have pushed home prices in Greater Boston and across the state to record highs.

The median sale price of a single-family home in the metro region was $585,000 in June, and for condominiums it was $505,000 — both records for the month, the Greater Boston Association of Realtors said Tuesday.

Statewide, home prices cracked new levels, as well, hitting $372,000 for a single-family home, breaking a record set in August 2005 during the last housing boom, according to data from the Warren Group. June’s $345,000 median condo price was also a record.

Prices in Greater Boston are also increasing at a much faster rate. The median sale price for a single-family home in the metro area was 4.5 percent higher than in June 2015, compared to just 1.9 percent higher statewide. Condo prices, meanwhile, were up almost 10 percent in the region, compared to 4.5 percent statewide.

“Unsatisfied demand drives up prices. It’s probably more acute in Greater Boston,’’ said Deborah Heffernan, managing partner at Avenue 3 Real Estate in Cambridge. “Our housing stock and pool is more expensive, so our median is pulled up.’’

But even at these levels, according to Warren Group’s chief executive, Timothy M. Warren Jr., the housing market is not in a bubble. Rather, Warren said, prices are reflecting strong demand and a very limited supply.

“Median prices are rising slowly. We’re not in a situation where prices are skyrocketing — at least not statewide,’’ he said.

Moreover, a separate index that follows housing prices around the country shows home values in Greater Boston are not growing as rapidly as in other major cities. The S&P/Case-Shiller Index, looking at sales recorded in May, found housing prices rose 5.6 percent year-over-year. That was slightly above the national average of 5 percent, but much lower than in Portland, Ore., where home prices increased 12.5 percent over the year, and in Seattle, at 10.7 percent, and Denver, at 9.5 percent.

“Most of the places seeing severe gains are mostly tech hubs; that’s what’s driving a lot of the significant increases,’’ said James Gulden, a Redfin real estate agent in Boston. “Boston has well-paying tech jobs, but there’s low inventory; that’s what’s going on in Boston.’’

Gulden said he expects prices to continue rising steadily.

“I haven’t made a bid in the past year that has sold for what it previously sold for,’’ Gulden said. “Every time it’s for a next higher price than what the previous buyer bought it for.’’

Sales activity remains heavy: The 7,387 single-family homes sold statewide last month marked the third-highest number in a single month since the Warren Group began tracking the data in 1987. At this time last year, there were 6,430 single-family homes sold in the state.

“There’s talk of rising interest rates,’’ Warren noted. “Just the talk of it makes people anxious and eager to get into the market and take advantage of those lower rates.’’

June marked the 13th consecutive month of increases in condo sales statewide, with 2,828sold. In the first six months, there were 10,673 condos sold in the state, compared to 9,337 in the first six months of 2015.

Phil Chaves, regional vice president of the metro Boston region for Coldwell Banker, said he is not surprised by the numbers, given the persistent shortage of available properties.

In 2005, “it was easy to have 50, 60, 70 homes available in a month, and now you’re lucky to have 10 to 15 active single-family homes. That’s huge,’’ Chaves said. “We bring it out on a Thursday, have the open house, then we’re looking at offers Monday at 5 p.m. or Tuesday at noon. That’s not unusual.’’

He said he expects the market to level off soon and that there is “no indication,’’ given more stringent lending practices, that a housing bubble is happening.

“The whole process is so different now than it was 11 years ago,’’ he said. “We just don’t have as much inventory to keep up with the demand.’’

Katheleen Conti can be reached at kconti@globe.com. Follow her on Twitter @GlobeKConti.