Two more holy crosses were allegedly desecrated by unidentified persons in South Goa's Loutolim village on 13 July, a police official said.
The locals in Loutolim, located around 40 kms from here, found the two crosses vandalised this morning, he said.
"The incidents seem to have happened in the wee hours," inspector Harish Madkaikar of Maina-Curtorim police station said.
One of the crosses is suspected to have been desecrated after 4 am today as a bread seller, who passed by the spot around that time, claimed to have seen the symbol intact, he said.
The two desecrated crosses were located at a distance of around 3 kms from each other, Madkaikar said.
A team of police personnel soon rushed at the spot and launched an investigation, he said.
Goa has witnessed a spate of attacks on religious symbols since early this month.
At least 11 holy crosses and a temple have been vandalised by unidentified persons in South Goa district since July 1.
Several gravestones were also allegedly damaged by unidentified persons at Curchorem town in South Goa on Sunday night.
The state Congress earlier demanded that the investigation into the incidents be handed over to CBI.
However, Vijai Sardesai, the leader of Goa Forward Party, which is one of the alliance partners in the BJP-led state government, had said that the local police was capable of investigating the cases.
In view of the incidents of defiling the religious symbols, Chief Minister Manohar Parrikar had last week held a high a high-level meeting with police officials.
He asked all the police stations in the state to form special investigation teams to nab the accused at the earliest.
The Goa Church also expressed a "deep pain" over the incidents of desecration of holy crosses.
The Church feels these incidents seem to be designed by vested interests to provoke communal discord in the state, which is known for religious tolerance.