The council, made up of past presidents, state governors and leaders of parliament, is "satisfied the security agents know very well where the girls are located," Gov Godwill Akpabio told reporters at a briefing.
The rescue of the girls was top of the agenda at the meeting, he said, and "military authorities also confirmed that efforts were being made and that very soon we will have good news."
The governor added the question is not whether the girls can be rescued but how to do it without endangering their lives.
Last week the Defence Ministry reported the detention of a businessman heading a "terrorists' intelligence cell" who it said "participated actively" in the Chibok abductions.
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Yesterday's council commended Nigeria's military and security agents, who have been roundly criticised at home and abroad for their failure to swiftly rescue the girls and to curb an escalating Islamic uprising by Boko Haram that has killed thousands.
Some 276 schoolgirls were abducted April 15 from a school in northeast Chibok town. Dozens escaped and 219 still are missing.
Boko Haram leader Abubakar Shekau has threatened in a video to sell the girls into slavery and as child brides if his demands are not met. In the video, some of the girls say they have converted from Christianity to Islam.
The extremists are believed to have divided the girls into smaller groups being held at different camps and possibly across borders in Cameroon and Chad, where sightings have been reported. There also have been reports that some of them have been forced to marry their captors.
Boko Haram which means "Western education is sinful" had attacked many schools and killed hundreds of students, some burned alive in dormitories.