Facebook chief executive Mark Zuckerberg has faced sharp criticism during the company's annual shareholders meeting about how the company operates, deals with violence and handles fake news.

Shareholders submitted five proposals critical of the company's top-heavy structure, as well as the way Facebook curates its content. All five were heard and rejected by majority vote; Zuckerberg controls more than 50 per cent of Facebook's shareholder votes.

Under fire: Facebook founder and CEO Mark Zuckerberg. Credit:Bloomberg

Arjuna Capital and Baldwin Brothers, two smaller investors, called on Facebook to publish a report examining the public policy implications of its guidelines around "fake news."

"To be clear, we are talking about content that is posted and disseminated with the intent to mislead, not the mainstream media, which the president refers to as fake news," said Natasha Lamb, Arjuna Capital's director of equity research and shareholder engagement. She added that Facebook needs to take clear action on the issue or risk alienating its audience. Lamb also spoke on behalf of a petition to have Facebook release information about its gender pay disparity, saying the firm is lagging behind its competitors on this front.