A key test of their unity would be on Sunday, at a protest rally in Delhi to which AAP has invited all opposition parties
The blaze happened in a building used to store firecrackers, an official in Delhi's fire service department said, adding that rescue operations were underway.
In December a fire swept through a rooftop restaurant in the Indian financial hub of Mumbai, killing at least 14 people, most of them women attending a birthday party.
Earlier in December, 12 people sleeping in the loft of a store in Mumbai died in a fire.