New York and Washington D.C. (CNN) Facebook's outgoing head of communications has taken the blame for working with a Washington, DC public affairs firm that spread opposition research about the social media company's critics.

"Responsibility for these decisions rests with leadership of the Communications team. That's me," Elliot Schrage wrote in an internal memo on Tuesday. "Mark and Sheryl relied on me to manage this without controversy," Schrage said. Facebook made the statement public on Wednesday evening.

Schrage announced earlier this year that he would be leaving the company.

Among the work the firm had done for Facebook, the Times reported, was to encourage reporters to examine the links between a campaign against the company and the billionaire liberal donor George Soros.

Facebook CEO Mark Zuckerberg told reporters last week that he first learned about his company's work with of Definers when he read the Times' story. After reading it, he said, "I got on the phone with our team, and we are no longer working with this firm."

Zuckerberg told reporters that the communications team was responsible for hiring the firm. A Facebook employee who asked not to be named told CNN that morale in Facebook's Washington, DC office, and the company more widely, is low, and that leaks to the media from Facebook employees have become more frequent.

"Clearly employees are questioning the mission of the company," this person told CNN.

Facebook did not respond to a request for comment.

In response to Schrage's internal memo, Sandberg wrote, "I want to be clear that I oversee our Comms team and take full responsibility for their work and the PR firms who work with us." Facebook made Sandberg's note public on Wednesday, as well.

Sandberg acknowledged that Definers' work was referenced in emails she had received.

"When I read the story in New York Times last week, I didn't remember a firm called Definers. I asked our team to look into the work Definers did for us and to double-check whether anything had crossed my desk. Some of their work was incorporated into materials presented to me and I received a small number of emails where Definers was referenced."

Schrage confirmed that Facebook asked Definers to "work on George Soros" in January 2018 after Soros called Facebook a "menace to society."

"We had not heard such criticism from him before and wanted to determine if he had any financial motivation. Definers researched this using public information," Schrage wrote.

Patrick Gaspard, the president of Open Society Foundations, which Soros founded, tweeted on Wednesday, "So @facebook decides to drop a turkey on Thanksgiving eve, with admission that Definers was tasked by company leadership to target and smear George Soros because he publicly criticized their out of control business model. Sorry, but this needs independent, congressional oversight."

Online criticism of Soros is sometimes explicitly anti-Semitic. Some of the backlash that followed the Times' report came from critics suggesting Facebook had engaged in dog whistle politics.

Responding to Schrage's memo, Sandberg wrote, "I also want to emphasize that it was never anyone's intention to play into an anti-Semitic narrative against Mr. Soros or anyone else. Being Jewish is a core part of who I am and our company stands firmly against hate," she wrote.

Definers said in a statement last week it was proud to have partnered with Facebook. "All of our work is based on publicly-available documents and information. The document referenced in the Times story regarding the anti-Facebook organization's potential funding sources was entirely factual and based on public records, including public statements by one of its organizers about receiving funding from Mr. Soros' foundation."