“As city leaders, we owe this to our youngest Angelenos to create safe spaces for them,” he said in a letter to constituents. “Our park facilities should be a safe haven, and we must do our part to provide the proper shelter for our kids.”

The letter was sent out as Mr. O’Farrell faces questions about whether his proposal was an overreach, impeding the activities of law-abiding adults who don’t have children and who might want to enjoy the pleasure of sitting in a playground.

“If you are worried that somebody is going to molest children, there are laws to prevent that,” said Peter Eliasberg, the chief counsel of the American Civil Liberties Union of Southern California. “You can’t just assume that because you’re an adult you don’t enjoy the sound of kids or watching kids in a playground.”

Mr. O’Farrell asked the city’s department of law to draft an ordinance based on his proposal. It would have to come to the City Council for approval before it could take effect.

Casey Revkin, a mother of a 2-year-old son who lives over in Silver Lake, said she supported Mr. O’Farrell’s initiatives. “I believe we can have sections of our parks designated for children and still have vibrant, diverse public spaces and communities,” she said