When Mark Zuckerberg takes employees’ questions during weekly all-hands meetings about Facebook’s role in society, he frequently turns to one of his longtime advisers, Elliot Schrage, to explain the social network’s thinking. Often, the company’s public policy and communications chief has been the one to outline Facebook’s strategy on crucial topics including the platform’s political influence and role in elections, according to two former employees.

Facebook’s reliance on Mr. Schrage is being tested like never before. Mr. Schrage, a 57-year-old lawyer, is in the middle of a fierce public-relations battle after a deluge of news that has regulators and journalists digging into whether Facebook has grown too powerful and data-hungry. As the scrutiny of Facebook has mounted, Mr. Schrage has had to toggle between apologizing for the company’s missteps and continuing to evangelize about the social network’s positive influence on the world.