The petition on AVAAZ.org asks people to sign "for the sake of all animals, especially the animals in the African region...where hunters are going for fun just to kill an animal".
Read more:
• Rich-lister's shocking animal slaughter
• US TV presenter blasted over smiling photo with lion she shot dead
Another petition, on the website change.org calls for Kendall Jones to be denied access to African states.
The photographs have provoked a similar response to one posted by US TV presenter Melissa Bachman who sparked controversy by posting a picture of herself next to a lion she'd just "stalked and killed" in South Africa.
Kendall Jones' critics have variously described her as "sick" and "depraved" for killing the animals and boasting about it online.
However, not everyone is offended. Her Facebook page has over 17,000 "likes" and frequently draws positive comments.
Ms Jones, who made her first kill, a White Rhino, on her second trip to Africa when she was 13, has also claimed that not all of the animals featured in the pictures are actually dead. Some have been tranquilized for educational use, she claims.
Her Facebook page states that she "is looking to host a TV show in January 2015," and repeatedly claims that her actions are best for the reserves and help control population numbers.
"Hunters are the biggest conservationists there are," she told the New York Daily News, adding "we want animal populations to grow and thrive!"
She wrote on Facebook that: "Funds from a hunt like this goes partially to the government for permits but also to the farm owner as an incentive to keep and raise lions on their property."
One particular image of Jones, posing with an endangered rhinoceros, incensed animal rights activists.
Jones defended the image saying that it showed a live animal: "The vet drew blood, took DNA samples, took body and head measurements, treated a leg injury and administered antibiotics."
"I felt very lucky to be part of such a great program and procedure that helps the White Rhino population through conservation," she wrote.
Despite her protestations Jones' Facebook page is full of negative comments. "I'd love to drop kick you into a lions' den, see how you do without your gun," one commenter writes.
Another Facebook user writes: "No matter how you look at it, seeing people smiling over the dead body of such a majestic animal is just sad."
Another is less diplomatic: "You are absolute scum. I hope a gorgeous African animal takes its own revenge on you one day for all the beautiful souls you have shot."
- UK Independent