Massachusetts is expanding its free coronavirus testing program to eight additional communities where positive test rates are above the statewide average at the same time the number of tests being conducted is dropping, Gov. Charlie Baker said Monday.

The testing initiative, which is also open for asymptomatic people who make an appointment, is expanding to Agawam, Brockton, Methuen, Randolph, Revere, Springfield, Taunton and Worcester, the governor said during a news conference.

“In addition to dozens of other testing sites in every county, we’re increasing our testing footprint to better understand exactly where the virus exists, who has it, and how we can follow up through our tracing program and other initiatives,” he said.

The overall positive test rate in the state has inched up recently from about 1.7 percent to about 2 percent.

The state is also closely looking at small clusters, including a private party in Chatham and an employee at Baystate Healthcare, who the governor said traveled to an out-of-state hot spot and was “lax” about wearing a mask. Other employees and patients have since tested positive, he said.

The Stop the Spread program was previously rolled out earlier this month in Chelsea, Everett, Fall River, Lawrence, Lowell, Lynn, Marlborough and New Bedford. So far, about 19,000 total tests have been conducted at the first eight sites.