The community centre group is made up of different religions
A pig's head has been nailed to the door of a former Methodist chapel which is being converted into an Asian community centre.
Police are treating the incident at Quenchwell, near Carnon Downs, Cornwall, as a racist attack.
The pig's head is the latest incident at the centre, which has been daubed with graffiti, including the words Leave Now, over the past two weeks.
Muslim owner Tipo Choudhury said he was "saddened and shocked" by the attacks.
Mr Choudhury, who has some Indian restaurants in Cornwall, said the centre would not be just about religion, but would enable people to celebrate their faith and culture.
"I think they have misunderstood the intentions behind the centre," he said, adding that it would not be a mosque.
The community centre group was made up of Muslims, Hindus, Buddhists and Christians.
He said the plans for the community centre would continue, but the situation was being assessed daily.
Insp Mark Richards of Devon and Cornwall Police said: "The graffiti is offensive not only to Asians, Asian religions, but also to Christians and Cornish nationalists whose name is taken in vain.
"It is totally out of order."