Islamist militants Boko Haram have released a video apparently showing about 130 girls kidnapped from a school in northern Nigeria on 14 April.
Boko Haram leader Abubakar Shekau said the children would be held until all imprisoned militants had been freed.
Interior Minister Abba Moro rejected the deal, telling the BBC that it was "absurd" for a "terrorist group" to try to set conditions.
Boko Haram abducted more than 200 girls and threatened to sell them.
The BBC's John Simpson in the northern city of Maiduguri says Boko Haram's comments show signs that the group is willing to negotiate.
Three of the girls - wearing full-length cloaks - are shown speaking in the 27-minute video, obtained by French news agency AFP.
Two girls say they were Christian and have converted to Islam, while the other says she is Muslim.
"These girls, these girls you occupy yourselves with... we have indeed liberated them. These girls have become Muslims," Abubakar Shekau says in the video.
He said his offer to swap the girls for imprisoned militants only referred to the children who had not converted to Islam.
It is thought the majority of the abducted girls are Christians, although there are a number of Muslims among them.
A man who is related to three of the abducted girls said the video at first gave him hope, but then made him anxious and tearful.
"Maybe they are converted into another religion by force, so it truly is a kind of terrifying situation," said the man, who did not want to be named.
Some 136 girls are shown in the video, just under half of the 276 pupils abducted from their school in the northern state of Borno.
Our correspondent says this could mean those abducted had been split into smaller groups to help avoid detection.
Local officials said they had started making copies of the video to show relatives and friends of the abducted girls in an attempt to identify them.
Boko Haram, which means "Western education is forbidden", had previously said the girls should not have been at school and should get married instead.
The militants have been engaged in a violent campaign against the Nigerian government since 2009.
The government has faced heavy criticism of its response to the mass abduction.
President Goodluck Jonathan said on Sunday that assistance from abroad had made him optimistic of finding the girls.
The UK and US already have teams helping on the ground in Nigeria and an Israeli counter-terrorism team is also on its way to the country.