Union carpenters are complying with leaders’ issuance of a stop-work directive for Massachusetts construction sites because of concerns that the job sites are breeding grounds for the spread of COVID-19.

The North Atlantic States Regional Council of Carpenters advised its 13,000 members to avoid Massachusetts construction projects until further notice beginning Monday.

“We’ve had a very positive response. It’s something the members felt was timely, and a lot of the contractors have responded in support of it,” council spokesman Bert Durand said today.

Gov. Charlie Baker has allowed certain categories of construction to continue statewide even as cities such as Boston and Cambridge ordered most projects to come to a halt. The Painters and Allied Trades Union also advised members to stop work at the end of Monday.

Baker’s order said housing construction, maintenance work and public works projects are considered “essential” categories and can go forward.

“The way the governor has structured his order, we believe it’s too broad and there are too many exceptions,” Durand said. “Projects are being kept open that are certainly not emergency projects or necessities.”

The council previously announced that two dozen members had tested positive for the coronavirus.

The governor’s office on April 2 issued a directive on social distancing and sanitizing procedures at job sites. Cities and towns are responsible for enforcing the new safety guidelines, or can require developers to pay for a third-party inspector. But Durand said the lack of supervision and enforcement remained an issue. 

“There’s no indication that it means anything more than words on paper,” he said.

Boston Mayor Marty Walsh took to Twitter Monday to urge developers and contractors to shut down construction sites during the coronavirus crisis.

“Even if your job site is allowed to function under the current guidance, if you don’t absolutely have to work right now, shut it down,” he wrote.