Fed up with high housing costs, activists and lawmakers plan to make a push for rent control Tuesday, but that idea was not embraced by the state's top elected officials after they privately huddled on Monday afternoon.

"I think the best way to deal with all issues around pricing is to increase supply," Gov. Charlie Baker told reporters when asked about rent control on Monday. "In Massachusetts we're decades behind where we should be with respect to building housing and creating more supply. We've added 600,000 people to our population in the last 20 years. We've added a fraction of the housing that would be required to support that significant increase in our population."

Baker noted the Legislature has provided resources for borrowing to boost housing, but said too many production proposals are dying at the local level. "All those resources don't do you a lot of good if you can't get anything done," said Baker, whose housing production bill remains stalled despite repeated attempts by the administration to advance it.

Rep. Kevin Honan, co-chair of the Housing Committee, on Tuesday told the News Service that he supports the governor's bill, but said the Legislature still has more work to do.

"This bill has local implications and ramifications, so we need to continue to build support," Honan said. "Some of our colleagues in certain communities are never going to be comfortable going from two-thirds majority to a simple majority. Nonetheless, though, we have a crisis in Massachusetts, so I support the bill."

Supporters of rent control legislation want the Legislature to permit cities and towns to institute the reform. On Monday, House Speaker Robert DeLeo and Senate President Karen Spilka gave voice to taking up a housing bill at some point.

If and when a bill emerges for House debate, House Speaker Robert DeLeo said he would expect some legislator to file a rent control amendment, but added, "I think probably most of our interest probably revolves around the issue of housing legislation as filed by the governor."

"We're looking forward to doing a housing bill," said Spilka, who declined to offer her opinion of rent control other than saying lawmakers would look at the idea.

Spilka had a rent-controlled apartment in Cambridge while attending school, she said during a Sept. 24 WGBH radio interview. Spilka attended Cornell University and Northeastern School of Law.