Facebook Inc.’s incumbent ad-buying shop GroupM has pulled out of the social-media giant’s agency review, the companies said.

Rival advertising firms Dentsu Inc., Havas Group and Publicis Groupe SA are still competing for the highly sought after account, which includes ad spending that could amount to more than $1 billion, according to people familiar with the matter.

Pulling out of the review will likely bring an end to GroupM’s work handling the bulk of the Facebook global media planning and buying business, although the agency group will continue to work with Facebook throughout the review process. GroupM’s Mindshare has supported the business across various Facebook brands since 2014. Dentsu also works on Facebook’s ad-buying account.

“We’re sorry that GroupM has decided to withdraw from the RFP [request for proposal] process; however, we look forward to continuing to partner with their talented team as we move forward with our review of global media capabilities,” a Facebook spokeswoman said.

Facebook works with several WPP agencies across its brands.

“While we will not be participating in the review, we look ahead to future opportunities building on the successful work we created together since 2014,” said a GroupM spokesman.

One reason for withdrawing from the review is a Facebook request for strict contractual terms, according to people familiar with the matter.

Contracts between agencies and marketers often require agencies to take on certain levels of liability or risk if an issue arises around the ad-buying process. Advertisers also often include terms around the right to audit an agency group.

GroupM and Facebook didn’t respond to requests for comment regarding Facebook’s contractual terms.

Advertisers in recent years have shifted larger portions of their budgets to digital marketing, which can involve complex systems, outside vendors and less transparency than traditional media buying. As such, advertisers also have pushed agencies to take on more liability around issues that could arise in the digital buying process, such as concerns around a data privacy breach or ad fraud.

GroupM is involved in a number of large pitches, including for Coca-Cola Co. , Unilever PLC, Bayer AG and Chanel, according to people close to the company.

ID Comms is the consultant supporting Facebook with its agency review process.

Write to Alexandra Bruell at alexandra.bruell@wsj.com