The victim, a girl from Jafrabad in north-east Delhi, died at Lok Nayak Jai Prakash (LNJP) Hospital on July 21.
At least 90 cases of dengue have been reported in the national capital this season out of which 38 were from the city and 52 from outside.
The sudden jump, a spike of 80 per cent over the last week, has now taken the number of vector-borne disease cases recorded this month to 62 till July 23.
"If it had happened at her residence, we would have owned up the responsibility. Also, main thing in dengue is platelet replenishment, since lives can be saved through that. Though we don't know the condition in which she was brought in, the hospital could have done better," he said.
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Delhi Health Minister Satyendar Jain asserted that the city government is prepared to face any situation and sought to blame the MCD for the rising cases of dengue.
"From our end, treatment aspect is on our side, and for that we are all prepared. Last year, we had 55 dengue clinics and this time we are trying to open 350. About 95 per cent of dengue cases can be treated at home and so we have tried to reach out to people through these special clinics," he said.
Asked if the first fatality reflects on the government's level of preparedness, Jain said, "Our government never claimed that dengue would be wiped out. No government or state can claim so.
Meanwhile, all three municipal corporations have stepped up anti-larval and preventive drives.
"We have distributed about 1.5 lakh impregnated (laced with special medicines) mosquito nets to people in our area. It is like a pilot exercise, and after gauging its efficacy, we may distribute it to all households," Nayyar said.
East Delhi Mayor Satya Sharma said, "We have stepped up our anti-dengue drive now. We have already distributed specially-made 1 lakh mosquito nets across our two zones."