Houston’s housing market recorded the third-highest sales total in the city’s history in June with record-high prices and fast-paced dealing continuing a torrid tone this summer.

The Houston Association of Realtors reported 7,220 single-family Houston area houses were sold last month. With records going back many years, the only times the monthly sales total was higher was in June, 2006 and this past May.

“The real (estate) market remains very, very, very strong,” said Amy Bernstein of Bernstein Realty. “There continues to be a strong demand and a small supply of homes for people to purchase.”

The recent uptick in mortgage rates has motivated many “fence-sitter” buyers to start pursuing a home purchase before rates go up some more, Bernstein said. Rates for 30-year mortgages are still below 5 percent, which is not high compared to the 1980s when rates were above 10 percent.

Buyers are also moving quickly now to get a home secured so they can register their kids for school, Bernstein said.

Sellers often receive multiple offers when they list their house for sale. Prices are going up, with record high prices reported in June.

The median price of a Houston single-family home — the midpoint at which half the homes sold for more and half for less — rose 13 percent to $192,000, up from $170,000 in June 2013, the Houston Realtors reported. The average price increased 14 percent year-over-year to $268,085.

June sales of Houston townhouses and condominiums increased 10 percent from one year earlier. A total of 604 units sold in June, compared to 548 properties in June of last year.

The low mortgage rates and Houston’s economic boom have been driving the housing surge. Houston, boosted by the energy business, has added 91,000 new jobs over the last year, one of the best job growth markets in the nation. June represented the 25th consecutive month that home sales have increased.

The inventory of homes for sale has been very tight. But the inventory did not tighten further in June. It remained unchanged in June from the 3.3-month level it reached in May. By comparison, the inventory of single-family homes across the United States stands at 5.1 months. Both represent very tight inventories. A six-month supply is considered a balanced market.

“The Houston housing market plowed full-steam ahead through another month and most Realtors I know have never been busier,” said HAR Chairman Danny Frank with Prudential Anderson Properties.

“The fact that inventory has leveled off month-over-month suggests that we may finally be starting to see enough homes listed for sale to keep up with demand.”