The airlift has been going on while land routes from Pakistan to the Afghan border remain closed in protest of a friendly-fire NATO airstrike last year that killed two dozen Pakistani soldiers.
The newspaper said Sunday the flights were an apparent violation of resolutions passed in Parliament banning NATO shipments of weapons and other "lethal" supplies through Pakistan.
Official Pakistani sources told The Express Tribune Pakistan's foreign office issued so-called non-objection certificates to the supply planes, which allows them to use Pakistani airspace. The foreign office agreed to issue the certificates under pressure from the Defense Ministry.
Pakistan and NATO have been negotiating a deal that would reopen the roads into Afghanistan, but an agreement is not considered imminent.