The minister made the statement amid a spate of attacks on religious symbols since early this month. At least nine crosses and a temple have been defiled since July 1 in several areas in South Goa district.
Last night, several gravestones in a Christian cemetery in Curchorem town were allegedly vandalised by unidentified persons.
"Those who desecrate Holy crosses are terrorists. This is an act of terrorism. We should treat them like terrorists. You don't go with arrest warrants to catch terrorists. You shoot them at site. Here also, those who are involved in such acts should be shot," said Sardesai, who is the mentor of the Goa Forward Party (GFP) which is one of the alliance partners in the BJP-led state government.
"Such things never happened in Goa and hence they are not able to detect these cases," said Sardesai in defence of police.
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Earlier in the day, the opposition Congress demanded a probe by the Central Bureau of Investigation into the incidents of desecration of religious places.
In the wake of the incident, Chief Minister Manohar Parrikar had recently given strict instructions to the police to increase patrolling around sensitive places in the state.
Two platoons of India Reserve Battalion were also deployed in South Goa to help local police in patrolling susceptible areas.
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