Nattarasankottai town panchayat councillor Nagarajan (50) and his son Vignesh (21) died on the spot when the gang of armed persons attacked them.
Nagarajan's wife was injured in bid to stop the gang from attacking her husband and son.
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She was admitted to a government hospital here and later referred to Madurai government hospital. Her condition was stated to be critical, police said.
However, the councillor's daughter, who has a three-month-old baby, was spared by the gang.
Special teams have been formed to nab the perpetrators who were yet to be identified.
Police said they were investigating whether previous enmity or some other dispute was the motive behind the murders.