It’s so far, so good in the implementation of a vaccine mandate for city workers and a proof of vaccination for certain indoor spaces, Mayor Michelle Wu said Tuesday.

“It’s been very, very smooth,” the mayor told the hosts of WGBH’s "Boston Public Radio," Jim Braude and Margery Eagan, saying her administration was going through “one by one” with every city employee who still needs to submit proof of vaccination for their jobs.

As of 8 a.m. Tuesday, 17,861 of the city’s 18,000 employees are in full compliance with the mandate, Wu said during a press conference about a new coronavirus testing site in Roxbury and additional sites opening soon in Dorchester and Mattapan.

About 1,000 city workers had received the vaccine since last Monday. Vaccine clinics are available at City Hall on Tuesdays and Thursdays, open to the public but geared toward city workers.

The Wu administration has also implemented a requirement for those aged 12 and over to show proof of at least one shot of a Covid-19 vaccine in some indoor spaces, such as dining, fitness, and entertainment venues. Places where you go in to pick up a takeout order or make a quick visit are exempt from the policy, which went into effect last Saturday.

The implementation of both the vaccine mandate and the proof of vaccination policy has gone relatively smoothly, aside from a vocal minority of people, including some first responders, who have repeatedly harassed Wu outside her Roslindale home and at press conferences.

Overall, 81 percent of Boston residents have received at least one dose of a coronavirus vaccine, a 36 percent increase from last week, according to city health officials.

The heartening numbers, and declining positivity rate, come as city officials have scrambled to increase local testing capacity after the holiday season, and gatherings around tables across the country, led to a spike in infections and high demand for tests. 

Wu and public health officials said testing sites are set to open at Dorchester’s Lilla Frederick Pilot Middle School and Mattapan’s Jubilee Christina Church.

The Frederick Pilot Middle School testing site, which opens on Friday, will be in service on Fridays (5 p.m. to 9 p.m.), Saturdays (noon to 8 p.m.) and Sundays (10 a.m. to 6 p.m.)

At Jubilee Church, which will open next week, testing will be available Tuesdays through Thursdays from noon to 7 p.m.

“We’re trying to open this resource for people and make it easy to access testing,” said Dr. Bisola Ojikutu, executive director of the Boston Public Health Commission.

Federal officials have also sought to ease access to tests, with people now being able to order free at-home tests online from the US Postal Service. Households can request four tests each.

The announcement of the Dorchester and Mattapan testing sites came at the opening of another free walk-in testing site in Roxbury, at the Bruce Bolling Municipal Building, which will turn around test results within 24 hours. The city’s other sites are at the Anna Cole Community Center in Jamaica Plain and the West End House in Allston.

The sites will be open “as long as they need to be,” according to Ojikutu, meaning they could remain in service beyond February if high coronavirus levels continue.

Ojikutu said she is “cautiously optimistic” about a waning surge, citing new data.

The city’s coronavirus positivity rate is now 26.5 percent, down from the previous week’s 32 percent. The threshold of concern is 5 percent.

“This is still very high,” Ojikutu said, noting that one out of every four people who have been tested are found to be coronavirus positive.

But overall, cases are down 33 percent, and emergency room visits have decreased 23 percent in the last week.

Still, hospitalizations of adults and children remain elevated, and Ojikutu urged people to get vaccinated, boosted, and tested.

At the state level, Gov. Baker announced that schools can sign up to receive at-home rapid tests for weekly use by students and staff. Schools that opt into the program are able to stop contact tracing, but have to keep participating in symptomatic or pooled testing.

School districts that join the program this week are expected to receive tests during the week of Jan. 24. Tests for students will come the week of Jan. 31.

The supply of tests comes from the 26 million units that the Baker administration ordered from iHealth. The state Department of Elementary and Secondary Education said the move would “enable school health staff to spend more time and resources identifying symptomatic individuals and focusing on other aspects of Covid-19 management.”

Separately, state lawmakers are pulling together a bill that would spend $55 million on testing, school mask supplies, and youth vaccination efforts. The bill sets aside $30 million for testing sites, and $5 million for vaccinating children ages 5 to 11.

Material from State House News Service was used in this report.