Workers were placing a concrete slab on the top floor of the seven-storey residential building in Uttar Pradesh state's Kanpur district when it came crashing down.
"Four labourers have been killed in the collapse and 17 have been rushed to a hospital with injuries," the area's top administrative official, Kaushal Raj, told AFP by telephone.
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Raj said the rescue operation would continue overnight "since there are some 30 more who are feared trapped under the debris".
Television footage showed earth-moving machines and soldiers using bare hands and mechanical diggers to remove mangled slabs of concrete and steel as rescuers in yellow hard hats rushed to the spot with stretchers.
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Home Minister Rajnath Singh took to Twitter to offer his condolences.
"I pray for the speedy recovery of the injured," Singh said.
The accident is the latest in a long line of deadly building collapses in India.
In December, nine people died when a building came down in southern India while under construction.
A massive influx of people to cities in search of jobs and a shortage of cheap housing have fuelled the construction of illegal buildings across the country, often with sub-standard material.
Millions also live in dilapidated old buildings, many of which cave in during heavy rains.
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