The state’s months-long positive trend in the fight against rapid COVID-19 spread has started to fray at the edges in recent weeks as the rate of new cases has ticked upward. Positive testing rates are nowhere near the 20 to 30 percent observed during the worst of the outbreak this spring, but they have inched up from about 1.7 percent in mid-July to more than 2 percent at the start of August, raising worries among some health experts that Massachusetts may not be able to sustain its pace along the path toward a new normal.

Gov. Baker could follow through on last week’s hints that his administration may scale down allowable gathering sizes if public health metrics did not improve. New Jersey Gov. Phil Murphy took a similar step Monday, albeit his state’s new limits mirror the existing ones in Massachusetts.

A top Baker official made clear over the weekend that many larger events that were common before the pandemic, particularly fans at sporting events and most live entertainment, are unlikely to return until there is a “medical breakthrough.”

After a few days where case counts were approaching or above 300, the Department of Public Health on Monday reported 165 new test-confirmed cases of COVID-19 and 10 new deaths. The 165 new cases came from tests of 12,278 new individuals, for a positive rate of about 1.3 percent.

Monday’s report showed a seven-day weighted average positive rate of 2.1 percent on July 30 and 31, and 2 percent on Aug. 1 and 2. That’s up from a low on 1.7 percent from July 11 through 14. Sunday’s report had shown a positive rate of 2.2 percent on Aug. 1.

The department adds testing information for previous days as it comes in, with some reporting lags from laboratories. The number of COVID-19 hospitalizations was at 375 in Monday’s report, down 31 from the prior day, with 64 patients in intensive care and 24 intubated.

South Boston Pop-up Testing – The next Boston neighborhood to get a rotating pop-up Covid testing site will be South Boston, Mayor Martin Walsh announced Monday. Tests will be available for free on a walk-up basis from Tues., Aug. 4, to Sat., Aug. 15, at Moakley Park, part of a partnership with the East Boston Neighborhood Health Center.

City officials have offered rotating pop-up testing locations to help residents in different neighborhoods access the resource, and the program comes to South Boston after previous runs in Roxbury and Allston. Both symptomatic and asymptomatic residents can get tested at no charge, though city officials encouraged pre-registration by calling 617-568-4500 to speed up the process. Covid testing is also available at more than 20 other locations in Boston.

Katie Lannan of State House News Service contributed to this report.