Of the total cases, 1080 are of those who have been brought to facilities through special operations, they said.
Government authorities had last month carried out measures to quarantine people who were connected with the large religious congregation that took place in Nizamuddin area in March.
By Tuesday night, the number of cases of the deadly virus in the city stood at 1561 including 30 deaths.
With two more fatalities reported, the death toll from COVID-19 in Delhi has jumped to 32.
Out of the total 1578 cases, 40 have been discharged and one has migrated out of the country, authorities said.
Meanwhile, sources said, an assistance ambulance officer of the CATS ambulance service "tested positive" for COVID-19 on Tuesday.
The number of containment zones in Delhi on Wednesday stood at 56.
Over 2,000 delegates, including from Indonesia and Malaysia, attended the Tabligh-e-Jamaat congregation in Nizamuddin West from March 1-15, and the south Delhi neighbourhood was virtually sealed earlier following fears that some people may have contracted COVID-19.
The civic authorities have carried out mass sanitisation and disinfection drives in hotspot areas in the last few days using drones and other measures.
Houses in containment zones are being surveyed by medical teams and people were made aware about the signs and symptoms of COVID-19, methods of prevention, social distancing measures, importance of hand washing, the department said.
House to house surveillance activities are being carried out in identified cluster containment zones, the Delhi health department said in a statement.
An order has been issued to all registered nursing homes and private hospitals that they shall not refuse treatment to any injured or serious patients brought to them for any reason, it said.
The guidelines for COVID Testing Centres (CTC), COVID Isolation Centres (CIC), COVID Health Centres (CHC) and COVID hospitals have been issued, authorities said.
Sample collection for the high-risk areas in identified containment zones for people who had come in contact with persons testing positive is being carried out, it said, adding, 692 samples have been collected till Tuesday.
According to the Delhi Health Department, out of the total 1,578 cases recorded so far, at least 867 are admitted at various hospitals like LNJP Hospital, GTB Hospital, RML Hospital, Safdarjung Hospital and Rajiv Gandhi Super Speciality Hospital (RGSSH) and AIIMS Jhajjhar, adding that 29 of them are in ICU and five on ventilators.
Total number of COVID-19 samples sent till date stands at 16,605, the Delhi Health Department said in the statement.
As many as 2,517 people have been kept in quarantine at various government facilities, it said.
As many as 30,451 people who came in contact with affected persons, are under home quarantine till date and 18,464 have completed their 14-day quarantine, they said. KND RDMRDM