Councilman Kallos said the Trump decision spurred him to action. He said he has wanted to ban disposable plastic water bottles since trying to buy one himself while visiting San Francisco several years ago and being told he could not. So he bought a reusable bottle to tote around — something he now does in New York.

“You see plastic bottles everywhere,” he said. “It makes New York look like a dump and we can do better.”

This is not the first time that New York has taken a stand against plastic bottles. In 2008, the office of the City Council speaker, Christine C. Quinn, stopped buying bottled waterfor Council offices. A 2009 state executive order barred state agencies from buying bottled water, to save taxpayer dollars and improve the environment.

The city has also targeted other plastic waste. In 2016, the Council sought to encourage shoppers to give up plastic store bags by charging 5 cents for most plastic and shopping bags. But that law was blocked last year by state legislators, some of whom argued that it imposed a regressive tax on the poor, and Gov. Andrew M. Cuomo.

Mr. Kallos and Mr. Espinal said their proposed ban on plastic bottle sales was more limited than the plastic bag fee and less likely to draw interference from state lawmakers.

Michael Whyland, a spokesman for the Assembly speaker, Carl E. Heastie, said that while Mr. Heastie, a Democrat from the Bronx, had not yet seen the proposed ban, “The speaker has always said that the city has the ability to enact a ban on unnecessary plastic waste.”

Mr. Kallos and Mr. Espinal said they will introduce bills next week to lay out more details about the proposed ban. Mr. Kallos said that vendors in city recreational areas could face penalties for selling plastic bottles, including possibly having their concessions revoked.