HCMC began social distancing for at least two weeks last week.
Director of its Department of Health, Nguyen Tan Binh, said at a meeting Monday that the city has "basically identified all infected areas and is continuing to track down everyone who had direct contact with confirmed patients."
In the latest wave that began in Vietnam on April 27, HCMC had had 437 cases linked to four clusters. The latest and biggest cluster was found on May 26 at a Christian congregation in Go Vap District.
The city imposed the government's Directive 16 in Go Vap and Thanh Loc Ward in District 12, while the rest of the city had to comply with the slightly less stringent Directive 15, which suspends social events, bans gatherings of 20 people or more anywhere and 10 or more outside of workplaces, schools and hospitals.
People should keep a minimum distance of two meters between each other in public places.
Directive 16 prohibits gatherings of more than two people in public and people can only leave home for emergencies, buying food and medicines or working in facilities and businesses that produce or sell "essential" goods.
City Party chief Nguyen Van Nen said the daily number of cases has fallen gradually, showing the preventive measures are working.
From around 50 cases a day in late May it has dropped to around 30 now.
"If the city had not imposed the social distancing order, the outbreak could have gotten out of control and no one can tell what could have happened by now," Nen said at the meeting.
City chairman Nguyen Thanh Phong said to protect public health the city had made the social distancing decision after serious consideration, reconciling itself to sacrificing economic development.
So, for the remaining one week too all related agencies and units have to work hard to control the outbreak.
"We should not ease any prevention measure just because the daily infection tally has dropped. We have to make the best of the 15-day social distancing period to stop the outbreak."
The health department estimated there would be 40-45 new cases daily in the coming days after doing a second test Sunday on people who had come into direct contact with patients.
"Most are in quarantine facilities or areas that have been isolated and so cannot spread the virus into the community," Binh assured.
Based on current developments, healthcare officials expect the outbreak to peak in two to three weeks, he said.
As of Monday, the city had 7,770 people in quarantine while 13,714 others are self-quarantining at home or elsewhere.