He 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.
‘We will hunt them down’
In a pre-recorded address broadcast on Tuesday, President 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, he 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,” the president said.
At the same time, he stressed that – despite the state of emergency – politicians in the three states would remain in their posts.
The president also admitted that the government was not in control of the whole country, the BBC’s Will Ross in Lagos reports.
This is not the first time he has declared a state of emergency, our correspondent adds, 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, Mr Jonathan had to cut short a trip to South Africa to deal with the growing violence.
Source: BBC
Nigeria president declares emergency
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Nigerian President Goodluck Jonathan has declared a state of emergency in three states after a spate of deadly attacks by Islamist militant groups. In a televised address, he said he had given the military powers to take over security in the states of Adamawa, Borno and Yobe.