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.

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.