Cardinal Malcolm Ranjith, the archbishop of Colombo, said the church may not be able to stop people from taking the law into their own hands unless the government conducts a more thorough investigation and prevents further attacks.
The cardinal said he is not satisfied in the manner in which the government has carried out its investigations so far.
Cardinal Ranjith told reporters: "All the security forces should be involved and function as if on war footing.
"I want to state that we may not be able to keep people under control in the absence of a stronger security programme.
"We can't forever give them false promises and keep them calm. (We ask the government) to implement a proper programme in order that the people don't take the law into their own hands."
More than 250 people were killed when seven Islamist suicide bombers blew themselves up, targeting worshippers in three churches and in three luxury hotels.
The victims included at least 40 tourists who were having breakfast at the hotels.
Two other suicide bombers died by triggering blasts - one to avoid capture by the police, and another at an inn he was staying.
Islamic State has claimed responsibility, and investigators are looking into the extent of their direct involvement with the local radicalised Muslims who carried out the attacks.
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