BOSTON (WHDH) - As new coronavirus cases and hospital admissions continue to surge, Mayor Martin J. Walsh on Thursday urged all Bostonians to remain vigilant as Massachusetts awaits a vaccine and to refrain from hosting or attending holiday parties this year.

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“The holiday season looks a lot different this year. We all want to be with the people we love and celebrate our favorite traditions, but we must remember that the coronavirus is still with us,” Walsh said during a news conference at City Hall. “Now more than ever, we must continue to stay vigilant and follow all the precautions to keep ourselves, our families, and our communities safe.”

Since Thanksgiving, Boston and communities across the Commonwealth have seen coronavirus cases skyrocket, Walsh noted.

For the week that ended Dec. 3, the city averaged 408 new positive test results each day, according to Walsh. The city’s positive test rate also jumped from 4 percent to 6.9 percent.

Boston Health and Human Services Chief Marty Martinez reminded residents that indoor parties — small or large — increase the chances of transmission of COVID-19 because of social distancing constraints.

“We need everyone to stay vigilant and do their part to slow the spread of this virus. Making the difficult choices to be apart this year may mean that you can spend many more years with your loved ones,” Martinez said.

Walsh and Martinez also asked Bostonians to avoid traveling.

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