Police have said they are also investigating the possible involvement of two previously little-known groups - National Thawheedh Jamaath and Jammiyathul Millathu Ibrahim.
Authorities have yet to confirm any arrests or injuries in the clashes, but videos circulated on social media showed mobs throwing stones at Muslim businesses, destroyed furniture inside homes, shattered windows and overturned vehicles.
President Maithripala Sirisena said in an interview with The Associated Press on Tuesday that Sri Lanka is now safe for tourists.
Government primary schools up to grade 5 are scheduled to open next week.
St. Anthony's was among the three churches attacked by jihadi suicide bombers in coordinated attacks that also targeted three luxury hotels in Colombo on April 21.
The officer said all will be prosecuted under emergency laws approved after the Easter attacks.
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Police media spokesman Ruwan Gunasekera said that the Criminal Investigations Department (CID) had found that the group had over 140 million Sri Lankan rupees in cash.
Police have detained 73 suspects for investigation since the bombings and have seized stocks of explosives, improvised explosive devices and hundreds of swords. "Sri Lanka hasn't shared any such information with us".
Sri Lanka was also receiving worldwide help, with foreign intelligence services working alongside their local counterparts, Senaratne added.
Police said two arrests were made and more suspects had been identified through CCTV footage.
Authorities in Sri Lanka have blamed the blasts on two previously little-known local Islamist groups - National Thowheed Jamath and Jamathei Millathu Ibraheem - whom they suspect had worldwide links.
"With the many lovely people we have around us, close friends, talented colleagues and our loving family we will come together through it".