They included six community cases, comprising three Singaporeans or permanent residents and three work pass holders, said the Ministry of Health (MOH).
There were also 13 imported cases who had been placed on stay-home notices upon arrival in Singapore.
Migrant workers living in dormitories made up the vast majority of the other cases. More details will be announced on Friday night.
On Thursday, MOH said that about 14,500 foreign workers are currently serving out their quarantine after the testing of all workers in dormitories was completed on Aug 11.
"These workers will be tested when their quarantine ends, and we expect the case counts to remain high in the coming days, before tapering down thereafter," said the Health Ministry in its Thursday statement.
No cases in the community were reported on Thursday.
Of the 68 new cases reported on Thursday, there were two imported cases - a Singaporean woman and a permanent resident who arrived from India between Aug 6 and 8.
They were asymptomatic and tested positive for the virus on Wednesday.
MOH said both of them had been placed on a 14-day stay-home notice upon arrival in Singapore, during which time they were tested.
Migrant workers living in dormitories made up the remaining 66 new coronavirus patients announced on Thursday.
Two clusters in dormitories were closed as the dorms have been cleared by the inter-agency task force and now house only recovered individuals and those who have recently tested negative for Covid-19 infection.
The average number of new daily community cases has come down from two cases two weeks ago to one in the past week.
The number of unlinked cases in the community has remained stable at an average of fewer than one case per day over the same period.
With 309 cases discharged on Thursday, 53,104 patients have fully recovered from the disease.
A total of 75 patients remain in hospital, while 2,878 are recuperating in community facilities. None is in intensive care.
Singapore has had 27 deaths from Covid-19 complications, while 15 who tested positive have died of other causes.
Globally, the virus outbreak, which began in December last year, has infected more than 22.8 million people. More than 796,000 people have died.
117 new Covid-19 cases in Singapore, including 6 in the community and 13 imported
