Police said they recovered bundles of currency believed taken in one of the bank robberies this week, five pistols, two revolvers and ammunition from a house where the suspects had been holed up, the Indian Express reported.
Closed-circuit television footage from banks near those that were robbed helped lead police to the suspects and their location, authorities said. The banks that were robbed did not have such CCTV cameras, police said.
"Our officials surrounded the house and knocked on the door, asking the inmates to identify themselves. But they opened fire from inside," police commissioner J.K. Tripathy later told a news conference, the Indian Express reported. "Officials then asked them to surrender, but they continued shooting. This is a crowded, congested residential area where there are a large number of civilians."
Two police inspectors were wounded in the ensuing gun battle, police said.
The suspects killed in the firing were all in their 30s. Chennai, formerly called Madras, is the capital of Tamil Nadu state.