Paul, 32, was killed in the wee hours of Saturday on the Alappuzha-Changanachery route in south Kerala, while he was traveling in a car along with some acquaintances.
Though the police have claimed that Satheeshan has confessed to his crime, political parties have accused the police of trying to cover up the facts.
Deputy leader of the Opposition in the state assembly, Congress leader Thiruvanchoor Radhakrishnan, has alleged that criminals carry out their activities with impunity across Kerala, and blamed Home Minister Kodiyeri Balakrishnan for the poor law and order situation.
State Muslim Youth League president K A Shaji has urged the home minister to clarify details about the murder, including information on the acquaintances who were traveling with Paul Muthoot when he was killed. Shaji alleged that two police officers involved in the case should also be investigated.