Long Island’s real estate market is rising. Don’t expect it to soar.

The local housing market in June posted some of the highest median prices in three years: $425,000 in Nassau County and $340,000 in Suffolk, according to the Multiple Listing Service of Long Island. Sales activity was brisk, with 2,048 homes changing hands, more than twice as many as in the doldrums of early 2009.

A shortage of homes for sale — plus buyers’ sense that mortgage rates will keep rising — has sparked “feeding frenzies” at some open houses, with sale prices occasionally exceeding list prices, said Marie Asher, an associate broker with Century 21 American Homes in East Meadow.

“The market has totally changed,” she said. “I don’t want to say it’s a seller’s market, but we’re heading that way.”

A close look at the Island’s housing market, however, shows signs of lingering distress among homeowners. That distress is likely to keep the recent sprint from turning into a marathon.

Nearly 1 in 10 homeowners with mortgages here owes more than their homes’ value. The number of initial foreclosure filings is on the rise, after a brief respite last year. Banks continue to impose tight lending standards on would-be buyers. And if interest rates jump much more, the higher cost of borrowing could choke off some buying.

Plus, the Island’s economy remains troubled. And home prices on Nassau’s South Shore, in particular, are still suffering the aftereffects of superstorm Sandy, which hit on Oct. 29.

“The housing market continues to recover from its recent lows, but a plateau is in sight,” said Irwin Kellner, Port Washington-based chief economist for MarketWatch.com. Prices could rise by 10 percent to 15 percent, but they are likely to level off next year as interest rates continue to climb, Kellner predicted.

To be sure, the local housing market is increasingly favorable to sellers — particularly in areas not damaged by Sandy.

Quick deal surprises seller

Dottie Weremeychik recently found a buyer for her late uncle’s four-bedroom Cape in Hicksville. The home was listed at just under $330,000 in March, quickly garnered four offers and went into contract within six weeks for close to the list price, to a family buying their first home, according to Asher, who handled the sale.

“I was totally shocked,” said Weremeychik, a Wantagh resident. “I was truly expecting the house to sit for a very, very long time.”

Some first-time home buyers say they want to jump in soon, before prices and interest rates rise further. The average rate for a 30-year fixed-rate loan recently hit 4.31 percent, according to Freddie Mac. The record low was 3.31 percent, reached in November 2012. In May, the average rate was 3.35 percent. Higher interest rates tend to put a damper on home sales, since they price some buyers out of the market.

For now, though, rising interest rates have delivered a jolt of activity. Buyers “are realizing that the bottom has been hit,” said Marianne Garvin, chief executive of the Community Development Corp. of Long Island.

That’s a belief shared by Wendy Brennan, a mother of three who hopes to buy a home this summer in Babylon Village, where she now rents an apartment. “I need to ensure that I get in now before it starts to get too crazy,” she said. “We love our neighborhood so we’re really trying to stay in the district, but everything that’s available to us at this point is in the flood zone . . . Finding a house within my price range with enough space for us is very, very, very difficult.”

LI housing prices rise but concerns remain.