The photo-sharing service saw many of its users threaten to delete their accounts after it announced it would have rights to sell their photos.
Instagram also wrote that by using its service, users agree that business or organisation can pay the company to use their name, photos and data without any compensation to the user.
Instagram users then took to twitter and other social media sites to express their outrage, while some threatened to delte their Instagram accounts.
A petition was also launched on Change.org by photographer Jennifer Cox.
"As a photographer I find these terms abusive, I am upset that after using Instagram for more than two years I am forced to make a choice between letting them take over the rights to my work or leaving the entire community I have grown so fond of," wrote Cox.
"But I know now that if these terms become effective, I will leave instagram without a second thought."
In a blog post titled, 'Thank you and We're listening,' Kevin Systrom, co-founder of Instagram said that legal documents are "easy to misinterpret."
"It was interpreted by many that we were going to sell your photos to others without any compensation," said Kevin Systom, co-founder of Instagram. "This is not true and it is our mistake that this language is confusing. To be clear: it is not our intention to sell your photos."
Systrom said that the company will be working to modify certain parts in their terms so users can clearly understand what will happen to their photos.
He also assured users that they would continue to have ownership over their own photos and full control over who can see them.
"Instagram users own their content and Instagram does not claim any ownership rights over your photos. Nothing about this has changed. We respect that there are creative artists and hobbyists alike that pour their heart into creating beautiful photos, and we respect that your photos are your photos."
The new terms will not go into effect for another 30 days which the company says is for users to have the "opportunity to raise any concerns."
Facebook had a similar situation this year and ended up having to pay a hefty sum after legal action was taken.
The social network handed over $10m to settle a class action lawsuit when the site used the faces of several users in sponsored story ads without their consent.
"The Instagram service agreement outcry has once again reignited the 'data/cost' debate," said James Lusher, social media specialist at Fishburn Hedges. "It's no secret that technology giants continuously look to stretch boundaries to stay ahead of the competition and offer users a fresh service. But the difficultly is in getting the balance between innovation and customer trust.
"As more and more companies, not just Facebook and Google, look to harness the benefits of mining 'big data', they need to be aware of the PR implications, and communicate how they intend to use this data transparently and responsibly.
"It's clear that there is still much scepticism from consumers and uncertainty over the real cost of a 'free' social media service. However, the media shouldn't simplistically accuse these companies. When used responsibly, data is an extremely powerful and beneficial asset to both brands and consumers; consumers just need to be able to locate the opt-out button."
Instagram was acquired by Facebook earlier this year and received $715m in the deal.
The deal was put on hold for several months due to investigations by the Federal Trade Commission and Office of Fair Trading, fearing the company could monopolise photo uploads.
In a statement about the Instagram purchase, Mark Zuckerberg said that it was an "important milestone for Facebook" as it was the first acquisition that had a product with such a large amount of users.
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