Long Island home sales surged last month and prices ticked up, as the number of homes for sale continued to fall.

Nassau County saw a 23 percent year-over-year jump in closed home sales, with 1,174 homes changing hands last month, according to a report Wednesday by the Multiple Listing Service of Long Island. In Suffolk County, 1,221 home sales closed last month, a nearly 22 percent rise compared with the previous July.

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With inventory dropping and buyers jostling for the most desirable homes, Nassau County's median price increased by 7.5 percent, to $435,000, and Suffolk County's median price rose by 3.1 percent, to $335,000.

In Suffolk County, the lowest-priced "entry level" homes are attracting the most interest, said Jerry O'Neill, owner of Coldwell Banker Harbor Light in Amity Harbor.

"The combination of bottoming out on prices and, maybe, rising interest rates have bumped some people off the fence," he said. "First-time buyers are saying, 'I'd better get in.' "

The average rate for a 30-year fixed-rate mortgage hit 4.4 percent last week, up from 3.59 percent a year earlier, according to mortgage giant Freddie Mac.

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The supply of homes -- as measured by the number of months it would take to sell all listed homes, at the current pace of sales -- has been dropping for five straight months in both counties. Last month, Nassau County had slightly more than a six-month supply of homes, down from nearly 10 months in July 2012. Suffolk had an 8.4-month supply last month, compared with 12 months a year earlier. A healthy housing market has about a six- to eight-month backlog of homes, according to brokers.

Even in areas damaged by superstorm Sandy, homes are selling, real estate agents said.

In Long Beach, the Multiple Listing Service reported 104 home sales from January through July, at prices ranging from $115,000 to $1.3 million, said Joyce Coletti, a real estate agent with Douglas Elliman in Long Beach. By contrast, the city had 77 home sales, at prices from $182,000 to $1.6 million, during the same period in 2012, she said.

"Long Beach is coming back," she said. "People are coming to Long Beach and buying. However, everybody is looking for a deal, so nobody's overpaying for houses."

In Suffolk County, in areas hit by Sandy, homes are selling at about a 15 percent discount due to fears that flood insurance premiums could rise or a big storm could hit again, O'Neill said.

"We still have activity in the flooded areas," he said. "Of course, the people are expecting, and getting, a discount."