A combination of rising prices and falling inventory marked a strengthening luxury property market in Greenwich, Connecticut, in the first quarter, according to a Douglas Elliman report Thursday.

The median sales price of 13 luxury single-family homes, which accounted for 10% of all the sales in Greenwich in the first three months, stood at $6.375 million. The luxury threshold hit $5.075 million.

Luxury sales prices saw a 13.8% increase compared to the first quarter of 2017.

More: Private Island off of Connecticut Returns to the Market Asking $8.7M

The average luxury sales price also rose 12% to $7.75 million at the end of March.

Luxury sellers are being more realistic about pricing, said Jonathan Miller, author of the Douglas Elliman report and chief executive of real estate appraisal firm Miller Samuel. That realistic pricing is leading to more sales and, in turn, price increases overall.

Meanwhile, luxury inventory in Greenwich, one of the most affluent towns in the U.S., fell sharply in the first quarter to 138, a 44.8% decline year-over-year, marking the sixth consecutive quarter with a year-over-year decline, as "aspirationally priced" listings expired and exited the market, Mr. Miller said.

More: An Early 20th Century Connecticut Estate With Lots of Modern Amenities

The three most expensive sales in the first quarter of this year all topped $11 million. The priciest sale was a five-bedroom, six-bathroom home on Glen Avon Drive, which was sold in February for $14.5 million, according to Mr. Miller.

In the overall Greenwich market, the median sales price for single-family homes grew 8.3% year-over-year to $2.205 million, while the median sales price for condos fell 4.3% annually to $718,438 in the first quarter.