The state reported Tuesday that the death toll from the coronavirus outbreak in Massachusetts had risen by 57 cases to 6,473, and that confirmed coronavirus cases climbed by 422 to 93,693, as key metrics that state officials are monitoring for reopening continued to show downward trends.

The Department of Public Health also reported 4,920 new tests had been conducted, marking a total of 545,481 in the state.

The seven-day weighted average of positive test rates showed a slight decrease to 8.6 percent on Monday, down from 8.9 percent a day earlier. It has dropped 70 percent since April 15, according to the state.

Meanwhile, the three-day average of the number of coronavirus patients in the hospital dipped to 2,136 on Monday, down from 2,179 a day earlier. It has dropped 40 percent since April 15.

The number of hospitals using surge capacity also continued a downward trend, staying steady at eight on Monday. That number is a decrease from early to mid-May peaks of 20, as well as a 62 percent drop since April 15.

The three-day average of COVID-19 deaths also dropped from 68 on Friday to 57 on Saturday, a decline of 63 percent since April 15.

The numbers come a day after the state allowed most offices, salons, and retailers to open with limitations aimed at slowing the spread of COVID-19.

Governor Charlie Baker on Tuesday said there had been a trend of a “significant decrease” in positive tests over the last two to three weeks.

But both Baker and Boston Mayor Martin J. Walsh said during separate news conferences on Tuesday that people must continue to take precautions — such as observing social distancing, wearing face coverings, and continuing to wash hands and surfaces — as the state moves forward with its reopening process.

“I want to remind everyone, there’s about a two-week timeline between infections and positive test results as people develop symptoms and get tested,” Walsh said. “If we want to keep the numbers going in the right direction, we have to keep doing. . . all of those things if we want to continue to move forward.”

Travis Andersen of the Globe staff contributed to this report.


Jaclyn Reiss can be reached at jaclyn.reiss@globe.com. Follow her on Twitter: @JaclynReiss Martin finucane can be reached at martin.finucane@globe.com

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