State lawmakers could soon be debating legislation intended to strengthen Massachusetts' already-tough gun control laws.

Debate on the bill unveiled by House leaders, including Speaker Robert DeLeo, in May could happen as early as Wednesday.

The legislation would for the first time give local police chiefs the ability to deny a license for rifles or shotguns based on suitability standards and extend federal restrictions for firearm acquisition to the state level.

It would also require background checks for all private gun sales.

Supporters are hoping to get the bill through the Massachusetts House and Senate and onto Gov. Deval Patrick's desk by July 31, the end of the Legislature's formal session.