Dozens of clips and photos uploaded to the app show wild or captive creatures being attacked or deliberately subjected to suffering or tormented.
Critics say the social-media giant has a responsibility not to feature anything that encourages copycat cruelty just so that account-holders may earn money or get likes.
Users say Instagram even has videos of pets being crushed, despite outrage over years about such cruelty being featured on social media.
Alan McElligott, an associate professor of animal behaviour at the University of Roehampton, told The Independent he had reported up to 40 posts to Instagram, requesting they be taken down – but only one had been removed.
They included a clip of two buffaloes fighting, controlled by ropes held by people. One of the animals flips over, crashing onto its back – something unlikely to happen in the wild.
Dr McElligott said this type of footage should not be published as entertainment.
“Ultimately those accounts are looking to make money by building followers,” he said.
“They encourage ignorant people to make similar vids, which means more animal abuse. And ultimately Instagram is making money from animal abuse.”
Animal lovers have described the clips as “vile” and “horrendous”.
Instagram has previously acted on complaints of cruelty, and now a search for certain terms such as #Tigerselfie brings up the warning: “Animal abuse and the sale of endangered animals or their parts is not allowed on Instagram. You are searching for a hashtag that may be associated with posts that encourage harmful behavior to animals or the environment.”
But Twitter users report that when they too have complained to Instagram about abuse posts they receive automated replies stating the videos “don’t go against community guidelines”.
Dr McElligott says he reports only videos in which animals were or could be under human control, and that featuring clips of abuse alongside those of animals killing prey in the wild makes the problem worse.
“There is a general ignorance problem – these posts get many ‘likes’ and people don’t even realise they are examples of abuse.”
Examples such as a dog fighting a cockerel could have been stopped, not filmed, he said. “Anyone concerned for their welfare would intervene, not think that it is a perfect movie for Insta instead.
“In the horrific tiger vs dog one, the tiger is chained and captive. Again, it is completely under human control.”
Animal-rights group Peta says Instagram is “a minefield of deceptive accounts that are actually promoting exploitative attractions” such as taking selfies with wildlife or elephant-riding.
It says accounts that encourage people to touch wild animals, feature them as entertainment or “unlikely animal friendships” are all exploitative.
Instagram also has certain accounts about “pets” such as nocturnal bushbabies, which could be harmed by bright daylight, experts say.
Johanna Gibson, a professor of law at Queen Mary, University of London, told The Independent: “It doesn’t matter to the mechanics of social media fame whether that traffic is positive or negative. Indeed, social media to a large extent thrives on notoriety. So there is actually an incentive for people to post such material,” she said.
If identifying the person committing an abuse offence is impossible, changing the “fashion” for such posts was an effective way to curb them, she said.
An Instagram spokesman said: “Our community uses Instagram to share their experiences and sometimes this includes content that some find upsetting.
“While we remove any content that encourages violence or abuse against animals, we do allow some content that depicts animals fighting, and we add a warning screen to content that is particularly graphic.
“We’re investigating the accounts brought to our attention.”
A new group called Suffering4Selfies is urging Instagram to ban any posts about unethical wildlife entertainment.