Suffolk County Executive Steve Levy yesterday put on the dog - or more precisely, more than two dozen pups of all shapes and sizes - to show support for a plan to more than double the number of public dog runs in county parks.The proposal, filed yesterday by Legis. Steve Stern (D-Huntington) and Jon Cooper (D-Lloyd Harbor), would create a committee to identify five new sites - adding to two dog runs at West Hills Park and two others planned at Coindre Hall and Blydenburgh County Park.

Levy and the owners unleashed the dogs at Blydenburgh, only to see the pets immediately make tracks toward the woods, where they played together.

“This will make for a lot of happy dogs and dog owners,” he said. “We have so much parkland, there’s no reason that we can’t have a little room to let dogs roam free and let owners enjoy the great outdoors.”

Levy, up for re-election, put his clout behind the measure after a meeting last month with a pet owners group, Long Island Dog, based in Huntington. Stern said the measure could be voted on in May.

L.I. Dog president Ginny Munger Kahn said the county’s 600,000 dog owners will applaud the initiative and said it would put Suffolk in the same “forward thinking” league with places like New York City, with 50 dog parks. “There’s real joy among the thousands of dog owners, and there’s thousands of tails wagging, too,” she said.

In the past, park rules banned dogs, but several legislators in the last four years have created runs at individual parks. The new proposal, which calls for fenced-in areas of 2 to 5 acres where dogs can roam free, would be the first to review all parks for the best sites countywide, Cooper said. Parks Commissioner Ronald Foley said such runs cost $15,000 to $20,000 for fencing, benches and fountains for humans and pets.

“There’s a big difference when you can let the dog off the leash,” said Irene Rabinowitz, of Selden, accompanied by her Australian shepherd mix, Sydney. “It’s very exciting to them to be able to run around.”