BOSTON — With the chorus of critics calling for the Cannabis Control Commission to pump the brakes on its rollout of an expansive legal marijuana industry growing louder, the top marijuana regulator said Tuesday the agency will debate later this month whether it should license only certain types of marijuana businesses to open July 1 and wait to license others.

Gov. Charlie Baker, House Speaker Robert DeLeo and others have called on the CCC to scale back the industry envisioned in its draft regulations — which includes marijuana cafes, delivery-only marijuana businesses, and the ability for establishments like cinemas and massage parlors to offer limited marijuana products — at least until an initial retail market takes hold.

"We're absolutely going to talk about that and if we do decide to not issue certain categories of licenses on day one we're not going to leave them open-ended, we'll say 'here's our timeline for subsequent rollout,' " CCC Chairman Steven Hoffman said Tuesday when asked if the commission would consider a phased rollout of legal cannabis businesses. "But we have not made that decision, we are going to have that conversation."

That conversation is slated to happen on the final days of February. The CCC has scheduled meetings on Feb. 26, 27 and 28 at which commissioners will discuss the feedback to the draft regulations and debate what changes should be made before the regulations are finalized.

On Monday, DeLeo said he agrees with many of the concerns Baker and his administration have raised with the CCC's draft industry regulations, including the worry that regulators have bitten off more than they can chew by trying to simultaneously launch several different categories of marijuana businesses.

"I feel that we're probably going a little bit quicker than I would like to see in terms of these other issues coming up whether they be selling door to door delivery, whether they be cafes or whatnot," DeLeo said Monday.

Asked Tuesday if there is anything wrong with slowing down the rollout of legal marijuana sales and the implementation of all the license types the CCC has contemplated, Hoffman said that is a decision that the CCC must debate as a commission.

"There are tradeoffs, I wouldn't say there is anything wrong with slowing down. Tradeoffs are giving people head starts in the marketplace and making it more difficult for others to enter later on," he said. "I'm not, again, saying it's a problem as much as that's the tradeoff that I think as a commission we're going to talk about when we get together two weeks from now."