Democrats allowed the Violence Against Women Act to expire last month, saying they wanted to come back with something new and better.

They released their proposal last week, saying they’ll push for enhanced protections for victims of cyberstalking, allow tribal courts to pursue cases on their lands against non-Indians, expand the uses of grant money, and create new categories of people banned from legally purchasing firearms.

The gun provisions are likely to be among the biggest fights, along with long-running disputes over gender identity and how transgender women are treated under the law.

Democrats are aiming for a floor vote in April.

“We must meet our obligation to help stamp out domestic abuse, violence against women and girls, and sexual harassment, and provide victims and survivors with the resources to recover and seek justice,” said House Majority Leader Steny H. Hoyer, Maryland Democrat.

But Republicans say Democrats got off on the wrong foot by letting the law lapse last month.

Republicans had wanted to include an extension in the package of 2019 spending bills, but House Speaker Nancy Pelosi balked. Republicans said she was trying to gain political leverage, figuring if the law was in place, there would be less impetus to work on Democrats’ changes.

“It was just all of a sudden taken and [Democrats] said ‘Oh, we’re going to go do this now,’” Rep. Doug Collins of Georgia, the top Republican on the House Judiciary Committee, told The Washington Times. “And we had honest, good faith efforts to work this out in a bipartisan, bicameral way.”

The Violence Against Women Act was originally passed in 1994 and instituted a federal framework and funding for a host of programs dedicated to helping victims of sexual assault, domestic violence, and other crimes against women. Among other programs, it led to the creation of the National Domestic Abuse Hotline.

It was last reauthorized in 2013 and extended tribal court powers in crimes involving American Indian women and explicitly affirmed that same-sex relationships and transgender women are covered.

Its lapse last month doesn’t have any immediate effects. Grant money can still be spent, lawmakers said.

Democrats dismissed complaints about last month’s jockeying.

“We need to get it done,” said Rep. Debbie Dingell of Michigan, a chief backer of the new gun limits. “We are where we are now and we’ve got to get this bill reauthorized.”

Her proposal would expand the denial of gun-purchasing rights to those accused of abuse in dating relationship. Currently the law denies firearms to those accused of abuse in a marriage, or couples who are divorced, live together or have a child together.

Ms. Dingell calls it the “boyfriend loophole,” and says those who believe they were abused in dating relationships deserve the same protections.

“Right now people don’t understand how easy it is for perpetrators of dating violence and those convicted to still get a gun,” she said at a press event last week. “People with a history of domestic violence should not have access to guns.”

Rep. Debbie Lesko, Arizona Republican, worried provisions like Ms. Dingell’s stray too far from the core of the law.

“I just want it to focus on protecting women against violence,” she told The Times. “So if it’s going into gun control and all kinds of other things that we had suspected that it might, then that may be a concern.”

Mr. Collins said Democrats will have to contend with the GOP-controlled Senate, where some of Democrats’ changes will struggle to gain traction.

“If we’re actually trying to protect all these classes of people in these bills, then you need something that will actually pass the Senate,” he said. “This will not pass the Senate.”

Democrats do have one Republican backer, Rep. Brian Fitzpatrick of Pennsylvania.

“Congress’ failure to reauthorize this critical legislation jeopardized the resources that millions of Americans rely on,” Mr. Fitzpatrick said at a press conference.