The Nigerian military reports that Boko Haram militants in the north-east of the country are "in disarray" and leaving the country in large numbers as a result of its offensive against them.
In a statement, it said 14 enemy fighters had been killed and 20 apprehended since Saturday.
The army added that three of its soldiers had died in the fighting.
The BBC's Will Ross in the capital Abuja says it is not possible to verify any of this information.
Meanwhile, there are reports of many civilians crossing into Cameroon and Niger as they fear getting caught up in the offensive.
Efforts have been made to close the borders but they remain porous and the army is said to be having difficulty distinguishing between the Islamist militants of Boko Haram and civilians.
Nigeria is waging its biggest campaign to date against Boko Haram in three north-eastern states, having declared a state of emergency there on Tuesday.
Our correspondent says that a possible sign of how well resourced Boko Haram has become is the army's claim that the rebels are trying to move scores of vehicles from its camps, which have been targeted in the offensive.
Saturday saw a 24-hour curfew imposed in parts of the city of Maiduguri, an important base for Boko Haram.
Last week, President Goodluck Jonathan declared a state of emergency in three north-eastern states - Borno, Adamawa, and Yobe - after a series of deadly attacks by militant groups.
US Secretary of State John Kerry has urged the Nigerian army to show restraint and not violate human rights as it pursues the militants.
Mr Kerry said there were "credible allegations" of "gross human rights violations" by the Nigerian military.
Last November, Amnesty International accused Nigeria's security forces of carrying out widespread abuses in their campaign against Boko Haram, including extra-judicial killings, enforced disappearances and torture.
More than 2,000 people have died in violence in Nigeria since 2010, most of which is blamed on Boko Haram.
The group, whose name means "Western education is forbidden", says its quest is to overthrow the Nigerian government and create an Islamic state.
There has been growing concern that Boko Haram is receiving backing from al-Qaeda-linked militants in other countries.
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