His comments came as police chief Chandana Wickramaratne said they have accounted for every individual involved in the April 21 attacks that killed 257 people at three churches and three luxury hotels.
In the video, a bearded man with Baghdadi's appearance says the Sri Lanka bombings were Daesh's response to losses in its last territorial stronghold of Baghouz in Syria.
"We have already identified all active members of the group and it's a case of now arresting them", Sirisena said, adding that there were a further 25 to 30 "active members" linked to the bombings still at large.
Government primary schools up to grade 5 are scheduled to open next week.
The authorities have blamed the Easter Sunday attacks, which also killed 42 foreign nationals, on two little-known local Islamist groups, the National Tawheed Jama'ath (NTJ) and Jamathei Millathu Ibrahim (JMI).
Police spokesman Ruwan Gunasekera said on Monday that Negombo was calm and curfew had ended at 7 am.
Police found bullet holes in the wall on one side of the grounds, as well as long tubes suspected of holding bombs, the officer said.
"Importantly, Sri Lankan security agencies themselves have ruled this out after investigation", a senior official in the security establishment, who did not wanted to named, said.
The Easter Sunday bombings that killed 257 people and wounded almost 500 were led by a local cleric who is known to have travelled to neighbouring India and had made contact with jihadists there.
Police have detained 73 suspects for investigation since the bombings and have seized stocks of explosives, improvised explosive devices and hundreds of swords.
"There are religious institutions which have been getting down foreign preachers for decades", Abeywardena said. "But we should keep in mind that the threat has not been completely neutralised because it is an issue of global terrorism". "We will pay more attention to them".
Just two days ago the cardinal had established the resumption of liturgical services in the churches of Sri Lanka, after the serious attacks on Easter Sunday against three churches and three hotels in Colombo.