More than two decades after voters banned local rent control, Gov. Charlie Baker signaled Tuesday he would not support a nascent push from several lawmakers to allow cities and towns to implement tenant protections, such as a limit on rent increases.

“Rent control will stifle the production of new housing,” Baker told reporters after a tour of the new DraftKings headquarters in Boston. “That’s exactly the wrong direction we should go.”

Instead, Baker said, state leaders should focus on how to encourage construction of new housing. One of the governor’s biggest pushes this session is a bill that would lower the threshold needed to make municipal zoning changes from a two-thirds majority of the relevant board to a simple majority.

“We don’t have a lot of inventory, and what we have ends up being really expensive, so that pushes people farther and farther away from where they go to school or work to find a place to live,” Baker said. “We need to build more housing, not less.”

Voters narrowly banned local rent controls through a 1994 ballot question, but Rep. Nika Elugardo and Rep. Mike Connolly plan to file a bill in the coming weeks that would once again allow it alongside other practices, according to a Tuesday report in the Boston Globe.

Supporters say a return to rent control without prior approval from the Legislature would help mitigate the region’s housing problems by preventing tenants from being priced out.

Elugardo and Connolly could not be reached immediately for comment Tuesday, but the Globe report indicated the bill they plan to file is more extensive than one (H 1316) proposed by Rep. David Rogers, who like Connolly is a Cambridge Democrat. Rogers’ bill was referred to the Committee on Housing in January.

House Speaker Robert DeLeo would not say Tuesday whether he would support or oppose one of the proposals, but he indicated he would like to see debate unfold.

“Relative to where we are relative to rent control, I think it’s important that I myself as speaker allow that to go through the process, allow it to go through the hearing process, make sure I listen to and hear all of my colleagues from around the state as to their position,” DeLeo said during an appearance before the Cambridge Chamber of Commerce. “Although, as you have stated, what had happened it failed at the ballot some years ago, I think it is important relative to not only that but many of the issues that we’re talking about that, again, that we go through that process.”

Colin A. Young contributed reporting to this story.