COLOMBO, Sri Lanka — The Islamic State claimed responsibility on Tuesday for the coordinated suicide bombings on churches and hotels in Sri Lanka, as the president of the traumatized nation promised to dismiss senior officials who had failed to act on warnings about the attacks.

As Sri Lankans buried the dead from the half-dozen Easter Sunday bombings that killed more than 350 people, the Islamic State issued a statement boasting of the suicide assaults. It also distributed an online video showing the person Sri Lankan officials suspect of having led the attacks.

In the video, the man believed to be the chief suspect, Mohammed Zaharan, a little-known extremist preacher from Sri Lanka, leads masked, black-clad disciples pledging fealty to the Islamic State.

There is no proof that the extremist group did more than provide encouragement for the suicide bombings, part of its decree calling for attacks on others considered infidels by Islamic State ideologues. But the release of the video via the Islamic State’s news agency, and disseminated through its network of online chat rooms, suggested that the attackers had access to the group’s core operatives.