SOUTHPORT, Maine — Searching for treasure buried beneath seaweed, a dozen children climbed tiny Kitten Island off Hendricks Head Beach on Thursday morning — unaware that the Board of Selectmen this week took action to ensure that future generations could continue the same summer adventure.

The cozy beach, wedged in a cove just past the Southport General Store, was listed for sale, along with its adjacent home, earlier this summer. For decades, the late Ruth Gardner allowed public access to the beach, according to Southport resident Anne Grimes. But when Gardner died, her three nephews listed the property — and the largest portion of the beach — for $1.4 million.

When summer resident Linda Murphy arrived this year and saw the “For Sale” sign, she resolved to ensure that public access was not lost. Murphy circulated a petition — supported unanimously by residents at a July town meeting — urging selectmen to do whatever was necessary to ensure access to the beach.

On Wednesday, selectmen announced that they offered the owners $1.25 million for the home and beach, Selectman Smith Climo said Thursday.

Steven Bornick of Legacy Properties Sotheby’s, who represents Gardner’s estate, confirmed that the property’s owners accepted the offer for the 2,400-square-foot home and beach on 3.5 acres.

The sale is contingent on a townwide vote scheduled for Sept. 18, Climo said Thursday.

“These things only come up once. Get it,” Grimes said of the beach. “It’s lovely.”

Sitting on a seawall Thursday eating chips and salsa, 10-year-old Nate Rideout said he and the other 30 or so students at Southport Elementary School head to the beach “all the time,” to swim at recess or catch lobsters and crabs.

Teacher Shawn Gallagher brought three boys for lunch on Thursday as part of the school’s summer program.

“We’re down here all the time,” he said. “Last year, we did a lesson on sandworms. [The school] is small enough that we can do impromptu lessons — pile the kids in a bus and head down. There are so many learning opportunities we can take advantage of because we have this.”

“It’s just part of the fabric of this place,” Murphy said.

Climo said that if voters approve the sale, the town would likely finance the purchase over a 10-year period.

He said the increase in property taxes to pay for the home and beach have not yet been determined. The town could decide to sell the house and retain the beach. And voters could still reject the purchase in September.

“But that’s what the people get to decide,” he said.

Residents in other midcoast communities are also taking action to retain public access to local beaches.

In Harpswell, residents have negotiated since 2011 to make sure a favorite Bailey Island beach remains available to future generations after the owners listed the property for sale. Several groups have worked to obtain an easement for Cedar Beach and then to allow use of an access road, The Forecaster reported.