"This land (Goa) is the land of peace. This land does not accept Muthalik," Parrikar told the Legislative Assembly while participating in a debate on the issue.
The Sri Ram Sene chief during his recent visit to Goa had said that he was keen on opening a branch of the right wing group in the coastal state.
Parrikar said that since ages Hindus, Christians and Muslims are living in harmony in the state and "communalism" cannot come to Goa.
In a veiled reference to Muthalik, the chief minister said by not inviting certain people here we are keeping "demons" at bay.
Invoking mythology to emphasise that Goa has been a peaceful state, Parrikar said, "Goddess Durga is known as Mahishasurmardini or Sherawali outside the state, but in Goa, she is called as Shantadurga, the peaceful incarnation of the deity".
The opposition is trying to corner the ruling BJP government over the issue of Muthalik's possibly entry to the state.
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Parrikar had yesterday told the Assembly that "stern" action will be taken against those who invite the chief of the right wing group to the state.
Independent MLA Vijay Sardesai had earlier alleged that the chief minister was not forthcoming on dispelling people's apprehensions about the possible entry of Sene.