BOSTON (WHDH) - Boston Mayor Martin J. Walsh said Monday that coronavirus data indicates Boston “may be on the verge of a downward slope” but the city is not yet ready to reopen and return to normalcy.

Boston is expected to surpass 10,000 coronavirus cases this week but the increase in cases per day has been fairly flat, Walsh said during a news conference at City Hall.

“We have hope as well in these numbers. The daily increase in cases has been flat for a little bit here,” Walsh said. “These are signs that we may be on the verge of a downward slope.”

The number of COVID-19 patients in hospitals across the city has also been declining, according to Walsh.

While there may be signs of hope, Walsh stressed that it’s not yet time to open the city up.

“We have to stay the course,” Walsh said. “If we don’t, we risk dealing with a second and even worse wave of this virus. For everyone’s health and safety, and for the future of our city, we must get this right.”

Walsh added that Boston is working to establish universal COVID-19 testing.

The state’s reopening advisory board continues to make “significant progress” in putting together a gradual, multi-stage process of lifting restrictions on businesses and activities, according to Gov. Charlie Baker.

Baker’s non-essential business closure order and stay-at-home advisory remain in effect through May 18.

Starting on Wednesday, any resident or worker who can not safely practice social distancing in public must wear a mask or face-covering. Violators could face a $300 fine.

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