Attacks on police
The fighting broke out on Sunday after police arrested several leaders of a group seeking to establish sharia, or Islamic law.
The group, known as Boko Haram - which means "Western education is prohibited" in the local Hausa dialect - has called for a nationwide enforcement of sharia.
Residents said members of the group, armed with machetes, knives, bows and arrows and home-made explosives, attacked police buildings and anyone resembling a police officer or government official in the city.
The violence spread on Monday to the states of Borno, Kano and Yobe, where fighters set fire to churches, a police station and a prison.
Yar'Adua said security forces were still working in Borno to bring the situation under control.
"The bad situation we have now is in Borno where the leader of the group is residing. We are going to launch an operation ... to flush them out," he said.
The deaths of 55 people in Bauchi and Yobe have been confirmed by authorities.
But journalists have reported seeing more than 100 dead bodies, with the Reuters news agency reporting 103 people killed in the past two days in the northern city of Maiduguri alone.
Isa Azare, a spokesman for the Maiduguri police command, said 90 of the dead were members of Boko Haram, Reuters reported.
Shettima Mustafa, Nigeria's interior minister, told Al Jazeera: "These [Boko Haram] people are well-educated; they ride jeeps, they watch tv, they talk on mobile phones.
"But they preach to their followers not to go to school and this is really surprising and I cannot understand."
Salisu Mohammed, a conflict management specialist, told Al Jazeera that Nigerian authorities should have acted sooner to stop the proliferation of Boko Haram.
"Many people have known of the existence of this group, silently and within the community, especially in the last year," he said.
"They are becoming more extreme because in the past there wasn't a major push in place to check their proliferation.
"They are taking advantage of a broken-down structural condition in Nigeria that people can take the law into their hands without getting reprimanded."
Boko Haram was founded in 2004, setting up a base dubbed "Afghanistan" in the village of Kanamma in Yobe, close to the border with Niger.
Abdulmuni Ibrahim Mohammed, a senior member of the group arrested on Monday, told Reuters: "We do not believe in Western education. It corrupts our ideas and beliefs.
"That is why we are standing up to defend our religion".