The sources said the troops were on patrol in the Damasak area of Borno on Monday when they encountered the militants. Seven soldiers were killed in a gun battle, 11 soldiers managed to escape but 13 - including the commanding officer, a major - were captured, they said.
"The major fought hard but in the end he was captured and his phone was taken by Boko Haram," said a security source who was briefed on the incident.
When the troops returned to their camp and tried to call the number, it was answered by someone who said he was a member of Boko Haram and that the major and other troops were in the group's custody, the sources said.
They said a military rescue team had since found the bodies of the seven dead soldiers but has not located the missing troops.
A Nigerian Army spokesperson did not immediately respond to a request for comment.
The Nigerian military has started an offensive against militants in the northeast this year, going deeper into areas that have been under the control of insurgents.
Despite repeated offensives, Boko Haram and its splinter groups have continued to mount large-scale attacks, exploiting difficult terrain, porous regional borders and a limited state presence in parts of the arid northeast.
Boko Haram, a jihadist group that emerged in northeastern Nigeria in 2009, has killed tens of thousands of people and displaced millions across Nigeria and neighbouring countries.
The group has since split, with one faction aligning with Islamic State to form Islamic State West Africa Province (ISWAP), which has increasingly targeted military bases in recent years.
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