After Gov. Charlie Baker announced Tuesday he would advise, not require, residents to wear face coverings indoors, some of the state's most powerful Democrats called on him to force stricter coronavirus protocols this winter.

In a statement, state Senate President Karen Spilka called on Baker to "reinstitute a statewide indoor public mask mandate," require proof of vaccination for indoor social venues and "achieve vaccine equity."

"Many communities, businesses and school districts have already instituted these measures to help save lives and they should be applauded. However, time is of the essence and a patchwork strategy will not lead to a healthier, faster recovery for Massachusetts," Spilka wrote.

Earlier in the day, U.S. Rep. Ayanna Pressley also urged Baker to adopt a mask mandate, expand testing and increase the state's vaccination efforts, especially in communities hit hardest by the pandemic.

"As we continue to experience a winter surge and are now faced with the new threat of the even more contagious Omicron variant, it is incumbent upon policymakers, at all levels of government, to act aggressively to center the public health and keep our collective constituents safe and healthy," Pressley wrote in a letter to the governor.

Baker told reporters at a Tuesday morning press conference he does not foresee returning to any kind of mandatory rules governing masks in public places. The governor said the widespread adoption of vaccines and boosters, teamed with more access to rapid testing, means the state will not have to reimplement strict mask requirements.

"I have no interest in putting a mandate on this issue, given all the tools that are available on a statewide basis on the people of Massachusetts," Baker said. "If locals wish to pursue alternative options, they can do so."

Baker has been unclear whether he or his Department of Public Health have the legal authority to issue a requirement to wear masks indoors. Lawmakers, including Spilka, could pass a law to force Baker's hand or explicitly grant him the authority to bring back the mask mandate outside of the emergency order. Legislators have suspended formal lawmaking until the new year and lawmakers involved in the public health debate say quick and decisive action is expected from the executive branch, not the legislative.

After issuing her statement calling on Baker to take action, Spilka's office did not respond to questions about any legislative solution to what she indicated was an urgent matter. House Speaker Ron Mariano did not respond to requests for comment on Baker's or Spilka's remarks.

Sen. Becca Rausch has been an outspoken critic of Baker's decentralized approach to containing the virus and lead a Tuesday press conference with medical experts urging him to adopt the group's action plan, which includes a mask mandate.

"We have grossly and inexplicably insufficient action from the governor to protect public health and ensure the hospitals and emergency rooms remain accessible," Rausch said.