Fifteen people were killed in the raids on churches in Garissa, a town near the border with Somalia.
Kenya’s border region has been tense since it sent troops into Somalia to pursue al-Shabab Islamist militants.
Adan Wachu, head of the Supreme Council of Kenyan Muslims, told the BBC the attacks were acts of terrorism.
“There are people out there who are determined to make Kenya another Nigeria,” Mr Wachu, who also chairs the Inter-Religious Council of Kenya, told the BBC Network Africa programme.
“It’s not going to be allowed to have a sectarian division in this country – whoever wants to do that will of course fail.”
Last October, Kenyan troops entered Somalia in pursuit of al-Shabab militants accused of being behind various kidnappings on Kenyan soil and of destabilising the border region
But since then, al-Shabab has been blamed for a further string of grenade and bomb blasts across Kenya.
The group’s officials have not responded to accusations that it was behind the Garissa attack.