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8 year oldIn a post on his Facebook profile Mr Zuckerberg said he hoped to announce measures to tackle fake stories "soon".
He said this work "often takes longer than we'd like in order to confirm changes we make won't introduce unintended side effects or bias".
And he said that more than 99% of content on Facebook "is authentic".
"Only a very small amount is fake news and hoaxes. The hoaxes that do exist are not limited to one partisan view, or even to politics," he added.
He said that made it extremely unlikely hoaxes "changed the outcome of the election in one direction or the other".
Mr Zuckerberg continued: "That said, we don't want any hoaxes on Facebook. Our goal is to show people the content they will find most meaningful, and people want accurate news.
"We have already launched work enabling our community to flag hoaxes and fake news, and there is more we can do here. We have made progress, and we will continue to work on this to improve further."
Some data has shown that fake stories were being far more widely shared on the platform than follow-up stories debunking the claims.
For an increasing number of people, particularly Americans, Facebook is becoming the primary source of news coverage.
The site's News Feed is specifically designed to show users content it thinks will be of most interest, creating what some describe as a "filter bubble" that reinforces a person's view without injecting differences in opinion.
Earlier this year, Facebook was accused of being anti-Trump after it was alleged its human moderators were favouring liberal stories appearing in people's "trending stories" box.
While denying that claim, the site did sack its human team, instead relying solely on an algorithm to determine which stories were shown to be most popular.
Mr Zuckerberg said any new changes to the way hoaxes and fake news were flagged up had to be taken with caution.
"This is an area where I believe we must proceed very carefully though," he said.
"Identifying the 'truth' is complicated. While some hoaxes can be completely debunked, a greater amount of content, including from mainstream sources, often gets the basic idea right but some details wrong or omitted.
"An even greater volume of stories express an opinion that many will disagree with and flag as incorrect even when factual.
"I am confident we can find ways for our community to tell us what content is most meaningful, but I believe we must be extremely cautious about becoming arbiters of truth ourselves."
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