Updated 3:27 p.m.

Gov. Charlie Baker has refused calls for dedicated COVID-19 vaccination clinics for educators, stoking the ongoing battle with teachers' unions.

"I am not going to be in a position where I take vaccine away from people who are extremely vulnerable, who have multiple medical conditions and are over the age of 65, to give it to a targeted population. We're just not going to play that game," Baker said a day after he dedicated four full days for teachers' exclusive use at the state's seven mass vaccination sites.

Teachers have been asking for doses to be put aside for a vaccine distribution system dedicated to educators that would deliver the shots in schools. Baker had rejected that idea and only agreed to let teachers under 65 become eligible for the current phase of vaccinations after the federal government made that authorization. Baker reversed course, he said, to avoid complicating the ongoing distribution system.

In an unusual move signalling the depth of Baker's conviction, senior advisor Timothy Buckley issued a rare public statement before the governor spoke Thursday at one of his regularly scheduled coronavirus press conferences, this one at the Reggie Lewis mass vaccination site in Roxbury.

"The administration implores the unions to do the math: The state only gets 150,000 first doses every week," Buckley said adding that the Baker adminsitration "does not support diverting hundreds of thousands of vaccines away from the populations most likely to suffer serious illness and most likely to lose their lives to COVID.” Baker's vaccination plan has been focused on the populations most at risk of serious illness or death from the virus.

Buckley, one of the governor's most senior advisors, rarely issues statements to the press. His authorship of Baker's message conveys how seriously the governor considers vaccinations. Buckley wrote that Baker's administration "is dismayed that despite reasonable efforts to prioritize educator vaccinations, the teachers’ unions continue to demand the Commonwealth take hundreds of thousands of vaccines away from the sickest, oldest and most vulnerable residents in Massachusetts and divert them to the unions’ members."

Although not part of Buckley's formal statement, the press office cited a recent Rockefeller Foundation report which said that "while more data should be collected, there has not been a community outbreak traced to an elementary school, and contact tracing studies have found that children are almost never the source in infection clusters."

Baker has maintained that schools can and should operate safely before most teachers are vaccinated by insisting on masks, maintaining social distance and through the use of frequent virus testing.

"If you follow the rules and you pursue the mitigation strategies that have been recommended by a whole variety of experts in the space, you can educate kids in person and do it safely. And that's all we're looking for," Baker said.

In a letter to Baker and his public health team, 48 lawmakers, both Democrats and Republicans, urged Baker to adopt the unions' plans to divert enough of new vaccine supplies to vaccinate all teachers expected back in schools. The lawmakers say the teacher's share of doses should come from any increases in supply from the federal government.

"Implementing the steps outlined above will ensure that we can take advantage of the increased supply when it arrives while also providing assurance to schools and families that the restart of in-person learning will happen as safely and successfully as possible," the lawmakers wrote.

Baker wants most elementary schools back in person five days a week by April, while federal officials have told Baker not to expect increases in vaccine supply until April, making the governor's plans incompatible with the unions' vaccination goals.

The fight over teacher vaccine priority is the latest in a long war between Baker and teachers' unions dating back to his election in 2014 and his championing of the unsuccessful expansion of non-union charter schools in 2016.