Facebook says it will continue to host a video of Nancy Pelosi that has been edited to give the impression that the Democratic House speaker is drunk or unwell, in the latest incident highlighting its struggle to deal with disinformation.

The viral clip shows Pelosi – who has publicly angered Donald Trump in recent days – speaking at an event, but it has been slowed down to give the impression she is slurring her words. Several versions of the clip appeared to be circulating.

The president’s personal lawyer, the former mayor of New York Rudy Giuliani, was among the Trump supporters who promoted the story. He tweeted – then deleted – a link to a copy of the video on Facebook with the caption: “What is wrong with Nancy Pelosi? Her speech pattern is bizarre.”

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Despite the apparently malicious intent of the video’s creator, Facebook has said it will only downgrade its visibility in users’ newsfeeds and attach a link to a third-party factchecking site pointing out that the clip is misleading. As a result, although it is less likely to be seen by accident, the doctored video will continue to rack up views. Facebook only took the action following inquiries from the Washington Post, which first reported the story.

Trump tweeted a different altered video of Pelosi, which aired on Fox Business network on Thursday night, and had been heavily edited to make it appear as if she was stuttering and slurring her language. The president captioned the tweet: “PELOSI STAMMERS THROUGH NEWS CONFERENCE”.

Giuliani posted an incoherent tweet in an apparent apology for disseminating the Facebook clip. Trump has neither apologized nor deleted his tweet. The White House did not reply to a request for comment.

Concerns have been raised in recent years about the impact of “deep fake” videos, where artificial intelligence technology is used to create disturbingly realistic videos. However, the Pelosi Facebook video shows that a low-tech approach can be successful. The clip, edited by an unknown producer, appears to have been created by simply slowing down raw footage – something that can be done in a matter of seconds on most smartphones – and then adjusting the pitch of her voice.

One version of the video, which remains live on a Facebook page entitled “Politics WatchDog”, has been viewed millions of times, attracting comments speculating on Pelosi’s health, supposed use of drugs, and other apparent ailments.

The viral success of the crudely produced video highlights the challenges in fighting online disinformation when individuals are willing to share material that backs their own political views, even when it is accompanied by warnings.

The administrator of the Politics WatchDog page polled readers on whether to remove the video, with most voting for it stay online. They defended the decision to keep the video live, insisting “it’s a free country”.

“Independent factcheckers that Facebook uses are pro-liberal and funded by the left,” Politics WatchDog added, insisting that the decision to upload the video was simply to allow the public to come to their own conclusion: “Just for the record, we never claimed that Speaker Pelosi was drunk. We can’t control what the people in the comments think.”

A Facebook spokesperson said: “There’s a tension here: we work hard to find the right balance between encouraging free expression and promoting a safe and authentic community, and we believe that reducing the distribution of inauthentic content strikes that balance. But just because something is allowed to be on Facebook doesn’t mean it should get distribution. In other words, we allow people to post it as a form of expression, but we’re not going to show it at the top of News Feed.”

Tom McCarthy contributed to this report