Three persons from the vigilante group have been arrested for the assault which was captured on a mobile camera by an onlooker and the video has gone viral.
One of the girls was assaulted again even after a police constable intervened, they said.
Karnataka Home Minister Ramalinga Reddy said police had taken prompt action and all the accused had been arrested.
He said there was a substantial reduction in vigilantism in the Dakshina Kannada district.
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Thecommunally sensitive coastal district has witnessed several similar cases of vigilantism in recent years, involving different communities.
Police said the girls, a Hindu and a Christian, had gone with their boyfriends from the other community to the Pilikula Park when members of the group spotted and confronted them.
The group led by one Sampath Shetty not only questioned them but beat up them up in public.
A constable deployed in the area who got information about the incident rushed there and brought the girls to the patrolling vehicle, the police said.
The Mangaluru police registered a case and arrested Shetty and his associates.