The newspapers said their delivery vans had been searched and vendors questioned across the country, and copies of the papers destroyed.
The newspapers and international media groups have condemned the actions as censorship.
But defense officials said it was a routine security operation and denied confiscating copies of the papers.
The Nigerian government and President Goodluck Jonathan are facing public pressure to do more to tackle a bloody insurgency by Islamist Boko Haram militants in the north.
The group has attacked the army, media and civilians and staged kidnappings, including that of more than 200 girls from a school in Chibok in April.
The raids come days after Nigeria’s information minister, Labaran Maku, warned the media not to give “free publicity,” saying they must “define the lines between the urge to report and the need to protect the interest of our nation.”
The Leadership, Punch, Nation, Daily Trust and Vanguard newspapers said the raids were carried out Friday and Saturday.
An editorial in Punch said one of its distributors witnessed “a group of heavily armed soldiers” storming the cargo area of the Murtala Muhammed international airport in Lagos and searching all the editions waiting to be sent out.
The commanding officer said they were acting on “orders from above,” said the paper, adding that papers were prevented from entering Ekiti, Oyo, Osun, Ondo and Edo states.
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