"We do not support those who commit violence in the name of gau raksha (cow protection). Action will be taken against those responsible," Mr Rupani said in an event organised by India TV.
"At the same time, the government is ensuring protection of cows for which we have a law, which is the strictest in the country. It also has the provision for life sentence," the Gujarat chief minister said.
Cases of groups of people stopping vehicles on suspicion of transporting cow meat have been reported from across the country in recent times. People have been beaten and some even allegedly killed by such vigilante groups.
The first incident of cow vigilantism was reported from Dadri in Uttar Pradesh in 2015, in which Mohammad Akhlaq was beaten to death after allegations that he had killed a cow. In July last year, four Dalit men were stripped, tied to a car and flogged in Gujarat.
As reports of similar incidents from other states piled up, Prime Minister Narendra Modi and his union ministers issued strong statements against cow vigilantism. Condemning cow vigilantes, PM Modi said, "I have seen that some people are into crimes all night and wear the garb of gau rakshaks in the day".
At the event today, referring to reported attacks on Dalits, Vijay Rupani said police are filing cases and taking swift action whenever such cases are reported. "It is our responsibility to protect Dalits... We are ensuring safety and welfare of Dalits in Gujarat. That is why they support the BJP," he said.
Mr Rupani said his government has started withdrawing cases filed against Patidars. "We have already withdrawn 300 cases so far," he said.