Long Island real estate prices climbed last month as buyers competed for a dwindling supply of homes.

In Suffolk County, houses sold for a median price of $350,000 in September, 5.4 percent higher than a year earlier, the Multiple Listing Service of Long Island reported Wednesday.

Nassau County home prices increased year over year by 5.8 percent, to $465,500, the listing service reported.

Across the Island there were 13,769 homes listed for sale last month, nearly 21 percent fewer than in the previous September, listing service figures show.

“If we get a new listing and it is priced properly, it sells pretty quick,” said Deborah Galligan, owner of Marylou Swan Realty in East Patchogue. In some instances, bidding wars will push prices over the asking price, she said.

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The housing market in Suffolk was busier than it was a year ago, with 1,379 closed sales, a 6.6 percent annual gain. The number of contract signings increased by 5.1 percent year over year.

Sales activity slowed in Nassau, as 1,214 homes changed hands, a decline of 1.1 percent from a year earlier. But in a sign that sales could rise in the coming months, the number of contract signings increased by 10.1 percent.

In Nassau it would take 4.5 months to sell all the homes listed for sale at the current selling pace. In Suffolk it would take six months. A balanced market has a six- to eight-month supply of homes, brokers say.

Local real estate brokers said more first-time buyers seem to be getting into the market. That could contribute to the decline in inventory, since those buyers are purchasing a home without putting another one on the market.

The 2007-2009 recession put the brakes on many young adults’ home purchases, but that’s starting to change, said Jerry O’Neill, owner of Coldwell Banker Harbor Light in Amity Harbor. That gives a lift to homes in the entry-level price range of $250,000 to $400,000, he said.

“Typically, years ago people in their early 30s already had their first-time house, and they were moving up,” O’Neill said.

But now, he said, “people are entering at a later age.”

Many first-time buyers are motivated in part by rising rental prices and low interest rates, Galligan said. The average rate for a fixed-rate, 30-year mortgage was 3.47 percent, down 0.35 percentage points from a year earlier, mortgage giant Freddie Mac reported last week.

Loans and grants aimed at first-time buyers and veterans also help, Galligan said.

A survey released this week by real estate company Zillow found that, nationwide, 47 percent of homes sold in the past year went to first-time buyers. That’s much higher than the National Association of Realtors’ most recent estimate of 32 percent. Experts said different survey methods could explain some of the difference.