Police have not provided a breakdown of how many were killed and wounded at each location.
The government has urged people not to speculate about who could be behind the attacks and restricted access to social media in the aftermath of the bombings.
No information has been given on the identity of the 24 people arrested.
Addressing reports that officials had had prior intelligence of forthcoming attacks, Mr Wickremesinghe said: “We must look into why adequate precautions were not taken. Neither I nor the ministers were kept informed.”