By Agence France-Presse
Three bodies have been pulled so far from under tonnes of concrete and metal from the building, which was still under construction when it gave way late Tuesday in Greater Noida just east of the capital.
Eyewitnesses and neighbours said one of those still missing was a one-year-old child from one of two families thought to be under the debris and who had moved in only days before.
"My friend was living here with his family since last Saturday. I spoke to them last night but have not had any contact with them since 9:00 pm," local resident Sandesh Kumar told Indian television news channel NDTV.
"I am just hoping they are alright," he said.
"We don't know exactly how many are trapped inside. We believe there are 12 people who may be trapped under the debris," regional chief fire officer Arun Kumar Singh told AFP.
Sniffer dogs were also being brought in to assist with the search.
The building collapsed onto an adjacent newly constructed four-storey residential building, authorities said.
Both are part of a residential complex in one of the many satellite towns dotted around Delhi growing fast to house the fast-expanding population of the 20-million-strong megacity and its environs.
Parts of Greater Noida are notorious for rampant and unregulated construction, with many projects flouting building regulations and cutting costs and corners with substandard materials.
Police arrested three people, including the landowner, over the latest accident.
"We are questioning them to ascertain the kind of partnership they had with the builder... Strict action will be taken against those responsible," local officer Avnish Kumar told AFP.
Building collapses are common across India, especially during the monsoon season from late June to September, although it was unclear whether this latest disaster was due to recent heavy rain in the Delhi region.
At least 18 people died in May when a flyover collapsed in northern India, crushing vehicles and passengers under tonnes of concrete. Last year at least 30 people were killed in Mumbai after a 100-year-old house caved in.