Boston has gone a week without a COVID-19 death, marking what Mayor Martin Walsh described on Tuesday as a "very encouraging" span.

Walsh said 25 new cases of the coronavirus logged Tuesday brought the city's cumulative caseload to 15,967 since the onset of the pandemic, and its death toll has held steady at 754 since last week.

Statewide, there have been 121,214 total test-confirmed cases and 9,141 deaths among people with confirmed or probable COVID-19 cases, according to the Department of Public Health.

In an afternoon press conference outside City Hall, Walsh discussed Boston's COVID-19 metrics and the dozen shootings that city police responded to over the holiday weekend.

After "a couple of weeks of decline," the city's positive test rate stands at 1.7 percent, Walsh said. East Boston continues to have the highest positive rate of any neighborhood in the capital city, at 8.7 percent as of Sept. 1. That number is down from 11.4 percent three weeks ago.

"That's a good way to see the numbers go," Walsh said. "We want to continue that downward trajectory, if you will, over in East Boston, with testing."

Walsh said city officials launched an "elevated outreach plan" three weeks ago, targeting East Boston with efforts like the distribution of kits with cleaning supplies and virus information, partnerships with churches, and messaging for people in multi-generational households about strategies they can use to limit transmission.