The Democratic-led Assembly on Tuesday moved to advance gun control legislation as Senate Republicans increasingly sound willing to compromise on the issue.

The measures, introduced at a news conference by Assembly Speaker Carl Heastie and Democratic lawmakers flanked by gun control advocates, are meant to close loopholes for gun ownership for people who are deemed a serious risk, those who have been convicted of domestic violence, expand background checks and end the legal possession of bump stocks.

“What does this say about us as a society if we allow unfettered access to guns?” Heastie said. “Thousands of lives have been stolen, yet very little progress has been made to move the national conversation forward.”

Republicans in the Senate moved an alternative package on Monday, voting for bills that would bolster school security and add armed resource officers in schools. Senate Democrats have sought to attach gun control legislation, much of it identical to what is backed by Assembly Democrats, as hostile amendments and were voted down.

The gun control debate returned to the Capitol after a shooting at a high school in Florida last month that killed 17 people.

Heastie, a Bronx Democrat, said he was open to some of the school security measures, but drew the line at adding armed personnel in schools.

“The point that we’re trying to make here and this is where we walk away from our colleagues in the Senate is we don’t think more guns is the answer,” he said. “We think it’s the wrong message to send to students that they have to be in armed places. It gives them a false sense of security.”

Still, a compromise is possible on the issue. Sen. Elaine Phillips, a Republican from Long Island, endorsed specific gun control measures including the bump stock ban and closing the loopholes on domestic violence convicts. Other Republicans in the Senate have not ruled out taking up legislation, either.

“I’m happy to hear that and when these things happen sometimes it shocks the system,” Heastie said. “I just think the place where there isn’t any room for us is putting the guns in schools.”