The co-founders of Instagram have announced their resignation from the company, amid reports that their departure might be due to an increase in meddling by Mark Zuckerberg, CEO of the site’s parent company, Facebook.

Kevin Systrom and Mike Krieger did not say why they were leaving their positions as chief executive officer and chief technical officer, respectively, of the photo-sharing service, just that they were leaving to explore their “curiosity and creativity again”.

Facebook’s shares were down 2.4% at $161.51 in early trading, knocking more than $11bn off the stock’s market value.

Instagram, which Facebook bought in 2012 for $1bn, has more than a billion active monthly users and has grown by adding features such as messaging and short videos. In 2016 it added the ability to post slideshows that disappear in 24 hours, a copy of Snapchat’s popular “stories” feature.

In a statement on Tuesday, Systrom said he and Krieger were grateful for “the last eight years at Instagram and six years with the Facebook team”.

Zuckerberg said in a public statement: “Kevin and Mike are extraordinary product leaders and Instagram reflects their combined creative talents. I’ve learned a lot working with them for the past six years and have really enjoyed it. I wish them all the best.”

Analysts said the departure of the pair may have been due to growing tensions with Zuckerberg over the direction of the business since Facebook bought Instagram.

“Our sense is the duo may have wanted to run Instagram more independently than their parent company wanted,” said Scott Kessler, an analyst at the research firm CFRA.

Instagram accounts for Facebook’s fastest growing slice of revenue. Founded in 2010 by Systrom and Krieger, who met at Stanford University in California, Instagram rapidly gained popularity as an iPhone-only photo-sharing service with a focus on square images tweaked with various colour filters.

Within two months Instagram had a million registered users, and 10 million by the end of the first year. Its rapid growth and user engagement caught the eye of Facebook, which was on the lookout for any services that might threaten its dominance of the social network space.

Just before going public, Facebook bought Instagram for $1bn – considered an eye-watering sum for a less than two-year-old startup with no revenue but 31 million mobile users.

At the time Zuckerberg said that Facebook was committed to running Instagram independently, saying: “The fact that Instagram is connected to other services beyond Facebook is an important part of the experience.”

For Facebook it was an important land grab in the shift to mobile, an area where it had struggled and a shrewd purchase of a service that could have rivalled its own product. Since then the service has added Snapchat-like disappearing videos and other features, has grown to more than a billion users and has added more advertisements.

Lynette Luna, the principal analyst at GlobalData, said she was not surprised the founders were leaving at a time when Facebook was “squeezing more advertising dollars” out of Instagram. “Facebook’s strategy has been to allow the companies it has purchased to operate independently to garner growth, and then monetise,” she said. “When they start monetising that’s when there’s a little conflict with the founders.”

She said the same thing happened with WhatsApp, with both founders leaving the company in the last year over disagreements about encryption and privacy. “It’s pretty typical. The founders are given independent creativity and it’s probably been pulled a little more to align with a monetisation strategy,” said Luna.

Om Malik, a partner at the venture capital firm True Ventures, noted in a blogpost that Instagram had become increasingly crucial to Facebook’s growth prospects at a time when user growth of the core Facebook platform was slowing down. Product launches such as Instagram Stories and Instagram TV encourage users to spend more time on the platform, which in turn creates more opportunities to sell advertising.

That Systrom and Krieger announced their departures at the same time was a “very political statement”, Malik told the Guardian. He said it was an indicator of conflict between Instagram and the leadership of its parent company. “I’m astonished they stayed this long. The peace lasted for seven years, but in the last few months things must have started to go wrong pretty badly,” he said.

Instagram has largely escaped Facebook’s high-profile problems over user privacy, elections interference and misinformation campaigns, but that appears to be changing. Facebook recently disclosed that it had deleted hundreds of pages across Instagram and its main social network linked to global misinformation campaigns intended to disrupt elections.

As regulators have pushed Facebook to tackle privacy, social media addiction and fake news, Zuckerberg has come under more pressure to monitor services beyond the core social network. But Facebook is also keen to increase engagement with that core, which has seen growth plateau and certain subsets of users become increasingly disenfranchised.

Instagram has remained a bright spot for the company. It is still seen as a more uplifting place than Facebook, escaping fallout from scandals such as that around Cambridge Analytica. It is popular with teenagers and young people, a demographic Facebook has had trouble keeping.

Instagram Stories is now twice as big as its Snapchat counterpart with more than 400 million daily users. WhatsApp’s Status, which is similar, is used by 450 million, while Facebook Stories was used by only 150 million in May this year.