Six birds had died on Friday. The Deer Park will remain shut until normalcy returns, authorities said.
Delhi's Animal Husbandry Minister Gopal Rai has advised the authorities to "deep bury" the carcasses and undertake necessary disinfection processes in the park.
Rai will visit the Deer Park on Sunday afternoon to take stock of the situation, a government statement said.
Earlier on Saturday, a rapid response team constituted by the Delhi government collected eight samples from live birds in the Ghazipur poultry market.
Apart from that, seven carcasses of birds were collected from different parts of Delhi on receipt of calls on the helpline set up by the Delhi government.
Rai had set up six rapid response teams on Wednesday to visit various places, including bird sanctuaries and poultry markets, to collect samples. He later increased the number of teams to 10.
All the samples will be sent to the central lab in Bhopal which had earlier confirmed that the virus strain found in the initial sample of birds was H5N8 avian influenza.
On Friday, Rai had visited Ghazipur poultry market and said that no indication of avian virus infection was found in the 2.2 lakh chickens that arrived in the market.
The first deaths of two migratory birds was reported on October 14 in Delhi Zoo, and six more birds were found dead the following day. One bird each died on October 17 and 19. On Thursday, eight more birds died in the city.