In a televised address, the president said he had given the military powers to take over security in the states of Adamawa, Borno and Yobe.
Goodluck Jonathan also ordered more troops to be sent to the north-eastern states.
Islamist group Boko Haram has been blamed for most of the violence, killing some 2,000 people since 2010.
Nigeria is also affected by a spate of conflicts over land, religion and oil.
In the latest violence, 53 people were killed and 13 villages burnt in central Nigeria’s Benue state on Tuesday.
The conflict, which started last week, is said to have been caused by a long-running dispute over land ownership between cattle herders and farmers.
In a pre-recorded address broadcast on Tuesday, President Goodluck Jonathan said: “What we are facing is not just militancy or criminality, but a rebellion and insurgency by terrorist groups which pose a very serious threat to national unity and territorial integrity.”
Referring to recent attacks by “insurgents and terrorists” on government buildings and killings of officials and other civilians, the president said that “these actions amount to a declaration of war”.
“We will hunt them down, we will fish them out, and we will bring them to justice,” he said.
At the same time, Goodluck Jonathan stressed that – despite the state of emergency – politicians in the three states would remain in their posts.
Goodluck Jonathan also admitted that the government was not in control of the whole country.
This is not the first time President Goodluck Jonathan has declared a state of emergency, but this is a clear admission that far from being weakened by the army offensive, the threat of the Islamist militants is growing.
Last week, Goodluck Jonathan had to cut short a trip to South Africa to deal with the growing violence.
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