The raids took place after the coordinated attacks on Easter Sunday, which killed 253 people, including many worshipers attending Easter Mass.
National Tawheed Jamath (NTJ), a local extremist group, was blamed for the bombings but did not claim the attacks. ISIS claimed responsibility, but no link has been found between the attackers and the terrorist group.
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Police are investigating possible civilian relations with suspected terrorists.
A wounded suspect fled on a motorcycle, and another suspected terrorist could also be on the run, Jayasekera said.
One of the six alleged suspected terrorists was identified as Mohamed Niyas, known to the authorities as a prominent member of the NTJ. In an earlier statement by the army, Niyas was identified as the brother-in-law of alleged leader of the Easter Sunday attack, Zahran Hashim.
The eastern cities of Kalmunai, Chavalakade and Sammanthurai remain until further notice, according to the police. The curfew for these cities was imposed after the shooting. Sri Lankan authorities have attempted to eradicate "sleeping" cells that could trigger another round of attacks, Prime Minister Ranil Wickremesinghe told CNN on Thursday.
Sri Lanka's President announced a "major search operation" in the nation.
"Every household in the country is under review," said President Maithripala Sirisena at a press conference. "The lists of permanent residents of each house are created to ensure that no strangers can live anywhere."
The tensions have marginalized the Sri Lankans.
Catholic Sunday Mass was suspended "until further notice" Sri Lanka, Archbishop of Colombo, Cardinal Malcolm Ranjith, announced on Friday. He said the move would ensure the safety of the worshipers, and the church would "try to introduce some worship services" as soon as better security arrangements were made.
The government called on Muslims to stay home for Friday prayers, and many mosques were closed. However, some mosques opposed the appeal and opened the midday prayers.
Both Christianity and Islam are minority religions in Sri Lanka, each accounting for less than 10% of the total population. The vast majority of the Sri Lankan population identify themselves as Buddhists.
James Griffiths of CNN and journalist Ajith Wickremesinghe contributed to coverage from Colombo, Sri Lanka.