YouTube offered a definitive response Thursday afternoon, saying the company had removed the videos because they violated “clear policies that outline what content is not acceptable to post.”

Twitter declined to comment. But sharing the video would likely not conflict with the company’s policies, which permit “inaccurate statements about an elected official” as long as they don’t include efforts of election manipulation or voter suppression. Several tweets sharing the video, often alongside insults that Pelosi was “drunk as [a] skunk,” remained online Friday.

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But Facebook, where the video appeared to gain much of its audience, declined Friday to remove the video, even after Facebook’s independent fact-checking groups, Lead Stories and PolitiFact, deemed the video “false."

“We don’t have a policy that stipulates that the information you post on Facebook must be true,” Facebook said in a statement to The Washington Post.

The company said it instead would “heavily reduce” the video’s appearances in people’s news feeds, append a small informational box alongside the video linking to the two fact-check sites, and open a pop-up box linking to “additional reporting” whenever someone clicks to share the video.

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That didn’t satisfy lawmakers such as Rep. David N. Cicilline (D-R.I.), who took to Twitter to demand that Facebook “fix this now!”

“Facebook is very responsive to my office when I want to talk about federal legislation and suddenly get marbles in their mouths when we ask them about dealing with a fake video,” Sen. Brian Schatz (D-Hawaii) tweeted. “It’s not that they cannot solve this; it’s that they refuse to do what is necessary.”

While Facebook’s actions might provide context and lower the rate at which people will happen upon the video while browsing the social network, they did virtually nothing to prevent the false video’s spread by people who have already seen it: Any user could still like, comment, view and share the video as often as they liked.

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In the 24 hours after The Post alerted Facebook to the video, its viewership on a single Facebook page had nearly doubled, to more than 2.5 million views. The video had also been reposted onto other Facebook pages, where its audience was growing even further.

The conflicting responses reveal a key vulnerability in how the Internet giants safeguard against viral lies and blatant falsehoods. The companies run some of the country’s most prominent and powerful sources of information, including for understanding political campaigns in the months heading into the 2020 presidential election. But they have shown little ability — and, in Facebook’s case, interest — in limiting the spread of falsehoods.

Facebook has resisted removing outright false information by citing free-speech concerns, a stand the company reiterated Friday. “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,” Facebook said in a statement.

Jason Kint, the chief executive of Digital Content Next, a trade group representing online publishers, said Facebook should take a more active role in policing and slowing the spread of misinformation.

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The site, he said, is reluctant to give too much power to fact-checkers or content moderators, and many pieces of content can often lapse into gray areas, where people’s perceptions of the material depend on their personal politics.

But with clearer distortions like the Pelosi video, the company should respond more quickly and decisively to potentially stifle the disinformation before it gains a life of its own.

“When they put it into people’s timelines and give it velocity and reach that it doesn’t deserve, they’re helping to spread it,” he said.

“Disinformation can spread faster than true information itself,” he added,” And these networks have bad actors — which, in a scary way on this one, involves people in very prominent positions — who can move disinformation so quickly. I don’t think the people who are charged with getting the truth out there are able to mobilize those networks in the same way.”

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President Trump on Thursday night tweeted a separate video taken from the Fox Business Network: a selectively edited 30-second clip focused on her pauses and verbal stumbles from a 20-minute official briefing earlier that day.

The videos fed into what Pelosi’s defenders have called sexist and conspiratorial portrayals of the health of America’s highest-ranking elected woman. They also resemble political videos that posed similar questions about Hillary Clinton’s fitness during the 2016 campaign.

Pelosi tweeted Thursday night that Trump was “distracting from House Democrats’ great accomplishments #ForThePeople, from his cover-ups, and unpopularity.”

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Facebook has an internal software tool to find and demote the distorted video’s online duplicates, but the company could not say Friday how many times the video had been reposted.

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With the company’s decision made, Facebook groups reiterated their interest in promoting the distorted video. The Facebook page “Politics WatchDog” — from where the video has been shared 47,000 times, often alongside false claims about Pelosi’s use of alcohol and drugs — hosted a user poll with the question: “Should Pelosi video be taking down?” When a majority voted “no,” the page posted, “The people have spoken. Video stays,” alongside an emoji of a wine glass.

The Facebook page’s owners did not respond to requests for comment. But in a Facebook post, they called The Post “fake news” and said the “independent fact checkers that Facebook uses are pro liberal and funded by the left.”

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Among the people who promoted the distorted video before Facebook responded: President Trump’s personal attorney Rudolph W. Giuliani. He tweeted a link to the Facebook page Thursday evening — “What is wrong with Nancy Pelosi? Her speech pattern is bizarre” — then deleted it minutes later. He later referred to it as a “caricature exaggerating her already halting speech pattern.”

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Giuliani said in an interview Friday that someone had texted him the video, and that he decided to share it after watching her for the past few weeks when he said she had been “talking funny.”

After his tweet, he said, someone else texted him that the video had been altered. “I couldn’t tell if it was doctored,” he said. “I could tell she was worse than a few days ago. So I took it down [just] in case.”