The accused, Francis Pereira, had told the police that he "casually" vandalised 12 crosses over the last fortnight with no intention to create an enmity, said a senior police officer.
The Christian religious symbol in at least 12 places and a temple had been vandalised in the South Goa district since July 1.
The police hoped that with Pereira's arrest, they would be able to crack over 150 cases of desecration of religious places reported from the state in the last 15 years.
"A police team spotted Pereira attempting to damage the cross. On seeing the policemen, he tried to run away but the police managed to nab him," the senior officer told PTI.
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"During the preliminary questioning, he admitted to have desecrated the crosses over the last fortnight," he added.
Talking to reporters at Curchorem town, Superintendent of Police (South) Arvind Gawas said, "We have cracked the biggest and longest-running case of desecrations in the state with the arrest of Pereira. With this, we will be able to solve over 150 cases of desecration of religious places, which were reported over the last 15 years."
Goa Chief Minister Manohar Parrikar, state Agriculture Minister Vijai Sardesai, Curchorem MLA Nilesh Cabral, Director General of Police (DGP) Muktesh Chander and senior police officers held a meeting today at the Curchorem police station, following Pereira's arrest.
Talking to reporters, Pereira said he had no intention to trigger an enmity with anyone by his act.
"I did it casually. Nothing was planned. I used to see a cross and hit it," he said.
Chander said during the interrogation, the accused told the police that he had a plan to continue desecrating religious places in the state.
Sardesai told reporters that the confidence of the people in the state police force as regards the investigation of the desecration cases was vindicated with the arrest of Pereira.
A number of incidents of attacks on religious symbols, especially of the Christian community, were reported in Goa over the last fortnight. Besides crosses, around 50 gravestones were also damaged in Curchorem village last Sunday.
The Goa Church had earlier expressed "deep pain" over the incidents of desecration of crosses and felt that the incidents could have been designed by vested interests to trigger a communal discord in the state, which is known for its religious tolerance.