He was speaking to BBC Sinhala Service about the violence that was triggered by the death of a Sinhalese beaten up a group of Muslims at Teldeniya town late February.
The minister said the investigations would be concluded soon and the culprits brought to book.
There have also been reports of Buddhist monks and Sinhalese having prevented attacks on mosques and Muslim businesses.
Thwarted four attacks at Nelligala
Wathurakumbure Dhammaratana Thera said he and the Sinhalese people were able to thwart four such attacks at Nelligala.
In social media, there were many posts that encouraged violence, including the picture of a monk expelling a Muslim pavement hawker.
Minister Madduma Bandara said any such complaints would be investigated and action taken.
He said that during visits to the affected areas, he was told by both Sinhalese and Muslims about Buddhist monks mediating to resolve the problems, as well as acting violently.
Asked if the violence could have been prevented had the law been enforced fairly, he said the law had taken its course in the past few years even against ‘ministers and Buddhist monks’.
Police looked on
Responding to allegations that police did not take action to prevent the spreading of the violence, he said what needed to be done now was to control the problem, and not to escalate it.
The situation would have been different had the police acted differently, he said, noting that two people had died and 12 sustained injuries, eight of them from the bomb incident.
Admitting considerable damage to properties, he said an organized group with links to politicians had carried out the attacks.
The law and order minister also said the government was considering a supervision of the social media to prevent its being used to spread violence and hatred.
Ninety nine per cent use social media for the good of the society, he said, adding that that segment is affected by the ban.
He expressed confidence the ban would be lifted soon.
Madduma Bandara added that laws would be formulated to prevent the use of social media for unlawful, racist and anti-government activities.