In a letter to Ms Swaraj, the senior congress leader said post-mortem and other formalities had been completed a week ago and the reason for not releasing the mortal remains was not clear.
Despite having the body for 23 days, the reason for not completing examination of the body examination was not clear, Mr Chandy said in a release.
Urgent steps should be taken to get the body released to the next of kin, he added.
Father Martin of the Carmelites of Mary Immaculate (CMI), belonging to Pulinkunnu in Alappuzha, was found dead at Edinburgh in Scotland where he was doing his PhD and working at a church.
His body was found on a beach two days after he was reported missing.