Several of the dead and injured persons in the tragedy are said to be from Vizianagaram and Srikakulam districts of Andhra Pradesh.
Naidu, who travelled to Chennai from Sriharikota in Nellore district after witnessing the successful launch of PSLV-C23 rocket in the company of Prime Minister Narendra Modi, consoled the victims of the building collapse, an official release said.
Sriharikota is about 100 km far from Chennai.
The death toll in collapse of the under-construction 11-storey building near suburban Porur in Chennai has risen to 17, even as a woman was pulled out alive, sustaining head injuries on Monday morning.
Naidu has assured the victims of necessary medical care and relief on a "war-footing", the release said.
Naidu has already announced an ex-gratia of Rs 5 lakh to kin of each of the deceased Andhra Pradesh natives.
He has also asked a team of officials to go to Chennai to supervise the rescue and relief operations.