"Although the people behind this activity attempted to conceal their identities, our investigation found that it was linked to employees of the ISPR (Inter-Service Public Relations) of the Pakistani military," he said.
Gleichner alleged ISPR employees were operating military fan pages, as well as pages on Kashmir, "general Pakistani interest", and local and political news including on topics such as arch-rival India''''s army and politicians.
Some 2.8 million accounts followed one or more of the pages, he said.
"Examples" included a post from a page called "Pakistan Army - the BEST", with an image purporting to show a crashed Indian fighter jet with text reading: "Indian air force has become a consistent failure which is evident from current embarrassment for India".
Others praised prime minister Imran Khan for promoting peace, or propagated unverified claims a Pakistani pilot had shot down five Indian planes.
"We are constantly working to detect and stop coordinated inauthentic behavior because we don''''t want our services to be used to manipulate people," Gleichner said.
An ISPR spokesman had no immediate comment when contacted by AFP.
Facebook also said it was removing 687 pages and accounts engaged in similarly "inauthentic" behaviour that were linked to India''''s opposition Congress party, which is contesting nationwide elections due to start on April 11.
Congress reacted cautiously, with spokesperson Manish Tewari saying the party "will need to verify the veracity of these reports".
A recent standoff between India and Pakistan saw a deluge of "fake news" hit social media, raising concerns over misinformation in the upcoming election in the world''''s largest democracy.