He said even after the arrest, police would continue vigil in places of worship.
"As of now it (series of desecrations) appears to be a solo act. But we can't totally rule out involvement of others... Or it need not be a participatory involvement but support of different kind," Parrikar told reporters in Vasco.
The Goa police has arrested a 50-year-old man in connection with the alleged desecration of holy crosses in South Goa district.
The Christian religious symbol in at least 12 places and a temple had been vandalised in the South Goa district since July 1.
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"As the chief minister and home minister, I was very confident that we will crack it (the cases)," Parrikar said.
"We were going in a very scientific way. We have done a lot of data mining, used technology, as well as many other techniques which normally an investigation agency uses," he said.
"You require to track movement of vehicles. All those aspects we have taken into consideration during the current investigation," the chief minister said.
"We have also taken into consideration which were the vehicles near desecration site visiting every day. All this data was mined and properly analysed," he said.