ALBANY—New York Gov. Andrew Cuomo and lawmakers are close to a deal on gun-control measures that would make New York the first state U.S. to pass new firearms restrictions after the Newtown, Conn., school shooting.

The package includes provisions to ban high-capacity ammunition clips, a stricter assault weapons ban and increased penalties for some gun crimes. It could be voted on as soon as Monday, said state Sen. Jeff Klein, the chamber's top Democrat in a power-sharing arrangement with Republicans.

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