BOSTON — Massachusetts House leaders Friday unveiled a revised version of a bill that would increase protections for transgender people, adding new language that could facilitate legal action against anyone who makes an “improper” claim of gender identity.

Members of the Legislature’s Judiciary Committee were being polled on House and Senate versions of the bill, ahead of likely floor votes in both chambers next month.

The bills would expand a 2011 state law banning discrimination against transgender people in the workplace and in housing by also banning discrimination in restaurants, malls and other public accommodations, including restrooms or locker rooms. It would allow transgender people to use public accommodations corresponding to their gender identity.

The language in the redrafted House bill appeared to be an effort in part to address concerns raised by some critics who contend the safety and privacy of women and children in bathrooms or locker rooms would be compromised under the proposed law. Supporters argue such fears are unfounded.

The push for the Massachusetts bill has intensified as LGBT groups decry recent developments in other states, including a North Carolina law that directs transgender people to use public restrooms corresponding to the sex listed on their birth certificate.

The redrafted bill would allow the state attorney general to provide “guidance or regulations” to law enforcement about legal action against “any person who asserts gender identity for an improper purpose.”

The state Commission Against Discrimination would also determine “when and how gender identity … may be evidenced.”

Rep. John Fernandes, House chairman of the Judiciary Committee, said the revisions offer additional guidance to transgender individuals and to businesses, without weakening the proposed law.

“We are 100 percent confident that the intent and integrity of the bill are protected,” said Fernandes, a Milford Democrat. “We are just trying to flesh out how people should guide their behavior.”

House Speaker Robert DeLeo, in a statement, agreed the changes strengthen the bill.

Opponents have cited fears that a male sexual predator could falsely claim to identify as a female to gain access to a women’s bathroom or locker room.

One group, the Massachusetts Family Institute, quickly dismissed the House redraft.

“This version of the bill is essentially the same as it still offers no protections to women and children who don’t want to be eyed by or exposed to naked men in locker rooms or other intimate spaces,” said Jonathan Alexandre, legal counsel for the institute.

He objected to giving Democratic Attorney General Maura Healey regulatory powers, saying Healey, an outspoken supporter of LGBT rights, has been dismissive of objections from the bill’s opponents.

Freedom Massachusetts, which advocates for transgender rights, said it was pleased to see the legislation advancing toward a vote after being stalled on Beacon Hill for years.

“We do have some questions about the redraft and we look forward to working through those in the next few weeks with lawmakers, added Matthew Wilder, a spokesman for the group.

Senate President Stan Rosenberg has tentatively scheduled debate for May 12 on the Senate bill, which does not include the new language offered by the House. The Amherst Democrat said it was “imperative” that lawmakers get a bill to Republican Gov. Charlie Baker’s desk as quickly as possible. No date has been set for debate by the full House.

Baker has not committed to signing the bill if it reaches his desk but has said he opposes discrimination in any form.