These include people from voluntary children's homes, crisis shelters and children's disability homes.
Staff engaged in community services for people with disabilities, such as sheltered workshops, day activity centres and special student care centres, are also being tested.
Lee said in a Facebook post that the tests are being done as part of expanded community testing efforts during phase two of Singapore's reopening after the circuit breaker.
The Ministry of Health had already announced on June 25 that Singapore's testing capacity would be ramped up as the economy reopens and more people are out and about.
As part of expanded testing, more people will be swabbed for Covid-19 infection, including those 13 and above who are diagnosed with acute respiratory infection and front-line staff interacting with travellers.
More regional screening centres are being set up to meet the anticipated increase in the number of people being tested.
On Monday, Lee also announced that the Ministry of Social and Family Development will conduct fortnightly tests on all staff and residents of facilities serving seniors from July onwards to monitor their health.
The tests will complement other measures in place to check the spread of the disease, including the mandatory wearing of masks in the homes and facilities, regular temperature and health checks, and frequent washing of hands and cleaning of high-touch areas.
Lee also said that previous tests of staff and residents of facilities serving the elderly had returned negative.
He said: "We are staying vigilant... I'd like to thank the staff, residents and clients of our facilities for undertaking these tests as we work together towards a new Covid-safe normal."
Mewanwhile, there were 202 new coronavirus cases confirmed as of Monday (June 29), taking Singapore's total to 43,661.
They include six community cases, comprising four Singaporeans and permanent residents and two work pass holders, said the Ministry of Health (MOH) on Monday.
Migrant workers living in dormitories make up the vast majority of the other cases.
On Sunday, a 15-year-old student at East Spring Secondary School was among 11 new Covid-19 cases detected in the community.
The student was tested as part of proactive screening of school students who are diagnosed with acute respiratory infection when they first see a doctor.
Since the onset of symptoms last Thursday, the student had not gone to school.
She was among the 213 new Covid-19 cases announced on Sunday, of which 11 were detected in the community.
Of Sunday's cases, 202 are linked to dormitories.
And of the 11 community cases, six are Singaporeans, including the secondary school student and a close contact of an existing case.
The other five community cases identified are work permit and work pass holders employed in essential services, and who were detected through MOH's screening processes despite being asymptomatic. - The Straits Times/Asian News Network
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