Army spokesman Sani Usman said troops destroyed more rebel enclaves and camps in the restive state of Borno, which has been worst hit by the six-year Islamist insurgency.
“The fight against the terrorists in the northeast is gaining successful momentum, with most of the camps falling to the Federal might,” he said in a statement.
A total of 62 people were rescued from around the town of Gwoza, which last year Boko Haram declared the headquarters of its caliphate but which it lost control of in March.
Some 77 men, women and children, most of them “haggard, dejected and obviously malnourished”, also arrived in the town of Bama on Saturday, Usman said.
One man picked up said he had his right hand cut off by militants in their Sambisa Forest stronghold in Borno last year, he said, adding that eight Boko Haram suspects surrendered to troops.
Nigeria’s military has claimed a series of successes against Boko Haram recently and on Friday said it had rescued 90 people and dislodged Boko Haram from two villages near Gwoza.
President Muhammadu Buhari in early August gave his new military commanders three months to defeat Boko Haram, after six years of violence, at least 15,000 dead and more than two million homeless.
Shekau has not been seen on video since February and until an audio message last month had not spoken since March, when he proclaimed Boko Haram’s allegiance to the so-called Islamic State group.
His absence sparked fresh rumours about whether he was still alive or had been deposed as leader, with other videos this year fronted by an unknown rebel under the name Islamic State in West Africa Province (ISWAP).
Shekau said in a 25-minute recording in Hausa and Arabic via social media: “They (the military) lied that they have confiscated our arms, that we have been chased out of our territories, that we are in disarray.
“We are alive, I am alive, this is my voice, more audible than it was before. This is Shekau.”
He added: “Buhari is a liar and has deceived you. The army spokesman is also lying. He and his footsoldiers always run helter-skelter whenever we come face to face with them…
“Buhari, you once claimed that you will crush us in three months. How can you crush us?”
Shekau directly refers to IS group leader Abu Bakr Al-Baghdadi, to whom he says he is “loyal and subservient”.
He also namechecks IS spokesman Abu-Mohammed al-Adnani and sends “greetings to the faithful in Yemen”, where there is also an IS “affiliate”.
There was no indication of where or when the recording was made but it appears to have have been in recent days.
Shekau talks of Buhari’s “deal with Hollande”, referring to the Nigerian president’s three-day visit to Paris earlier this week, which included talks with his French counterpart Francois Hollande.
He also dismissed as untrue Buhari’s comments about “our brethren in prison”.
Buhari this week said the Nigerian authorities were talking to Boko Haram prisoners in their custody and could offer them amnesty if the group hands over more than 200 schoolgirls abducted last year.