Nigeria's military has located more than 270 girls kidnapped by the militant group
"The good news for the parents of the girls is that we know where they are, but we cannot tell you," he said.
Badeh ruled out a forceful military operation to free the girls, amid reports of secret negotiations to secure their release.
"We can't go and kill our girls in the name of trying to get them back," he said after demonstrators marched to military headquarters in Abuja, the capital, a few days after trying to march to President
Badeh offered no information as to how the military planned to recover the girls, other than to rule out force.
"We want our girls back. I can tell you we can do it. Our military can do it. But where they are held, can we go with force?"
Jonathan and ministers have publicly ruled out negotiations with the radical Islamist group, which would run counter to the country's anti-terrorism law. Most analysts say any military operation to try to rescue the girls would probably end in mass casualties.
Jonathan said Sunday that Boko Haram must release the girls unconditionally.
"We must rise up to tell them that they cannot defeat us, they must release our sisters back to us unconditionally," he said. "Our security men are working. Their mission is to ensure that Nigeria is a safe place and what Nigerians should do at this time is pray for them and support them."
Badeh rejected criticisms of the military.
"Nobody should come and say the Nigerian military does not know what it is doing. We know what we are doing," he said.
Authorities are stung by the protests and a viral Twitter campaign, under the hashtag #BringBackOurGirls, that have focused international attention on Nigerian military failures to protect the population in the country's northeast.
Hundreds have died this year, with almost daily attacks on Muslim and Christian villages in the region.
Nigeria's Premium Times reported last week that the military knew where the schoolgirls were, citing senior military officials.
U.S. officials this month pointedly derided the Nigerian military in comments to the Senate Foreign Relations Committee, describing the forces as "afraid to even engage."
Defense Secretary Chuck Hagel expressed doubt in comments on television about whether the Nigerian military was capable of rescuing the girls. "That's an open question," he said May 15.