Twitter has hidden some of Donald Trump's first tweets the day after a US election which remains undecided.
In one, the President wrote his vote advantage in key Democrat-run states had "started to magically disappear", and in another that 500,000 votes in key states were at risk.
The messages are now hidden behind warnings that say the claims are disputed and might be misleading.
The moves also limit users' ability to like and reply to the posts.
Twitter had earlier taken similar action over a post in which Trump said for the first time that his opponents "are trying to steal the election".
Facebook has added fact-check boxes to some of the messages on Mr Trump's profile on its platform, clarifying that final results might take longer than normal - but did not restrict engagement.
'Censor and silence'
One of the tweets said: "Last night I was leading, often solidly, in many key states, in almost all instances Democrat run and controlled.
"Then, one by one, they started to magically disappear as surprise ballot dumps were counted. VERY STRANGE."
He followed that with: "They are working hard to make up 500,000 vote advantage in Pennsylvania disappear - ASAP. Likewise, Michigan and others!"
Twitter took just over half an hour to react on each occasion.
Mr Biden's first tweet of the day said "we won't rest until everyone's vote is counted".
Twitter has not acted on any of Mr Biden's tweets.
But it has hidden a post by the chair of Wisconsin's Democratic Party Ben Wikler who posted that "Joe Biden just won Wisconsin".
On Tuesday, the Trump campaign claimed that "Silicon Valley continues its campaign to censor and silence the president".
Facebook has also been automatically adding labels to all recent posts on Trump and Joe Biden's accounts.
They inform readers that votes are still being counted and that the winner of the US presidential election has not been projected.
Facebook has begun placing notifications at the top of the timelines for all US users, explaining that the election had not yet been decided.
"Once President Trump began making premature claims of victory, we started running notifications on Facebook and Instagram that votes are still being counted and a winner is not projected," it said.
Once President Trump began making premature claims of victory, we started running notifications on Facebook and Instagram that votes are still being counted and a winner is not projected. We're also automatically applying labels to both candidates’ posts with this information. pic.twitter.com/tuGGLJkwcy— Facebook Newsroom (@fbnewsroom) November 4, 2020
Twitter said it had labelled Mr Trump's tweet about the election being "stolen" because it violated the firm's civic integrity policy.
But the network appears to be allowing some claims of victory, despite warning that it would not.
An earlier tweet from Mr Trump that he had enjoyed "a big win!" has been left untouched, as has a carefully-worded tweet from Mr Biden that said "we believe we are on track to win this election".
Analysis: Time for false claims to grow
By Olga Robinson, disinformation specialist, BBC Monitoring
It's been a busy 24 hours on social media. There's been numerous unsubstantiated or false claims about election fraud, voter intimidation and conspiracy theories about attempts to steal the election doing the rounds.
And we are likely to see more misinformation like this in the days to come.
The delay in announcing the final result means a lot for time for misleading claims to flourish online.
Conspiratorial claims about rigged elections can spread like wildfire, in particular if they are amplified by politicians and online influencers.
Premature claims of victory - like the one President Trump made while votes are being counted - can further fuel misinformation and potentially impact how people perceive the final result.
This is exactly what some experts have been concerned about: that viral misinformation about voter fraud and "rigged" elections might have the potential to undermine people's trust in democratic process for years to come.
The clampdown comes after months of preparation for a disputed election.
The social media firms have overhauled their policies to deal with false claims of victory and other misinformation about the vote.
Both Twitter and Facebook said they had suspended a range of recently created accounts.
Twitter said the accounts it targeted had violated its spam and manipulation policies - particularly those that seek to artificially influence online conversations.
YouTube also shut down live-streamed fake election results which were being broadcast via several accounts on its platform.
3/ Before the video was taken down, it rose to become one of Google’s most widely circulated videos in swing states. This underscores how platforms have continued to struggle with misinformation despite the development of new policies. https://t.co/g0TGlpvyr4 pic.twitter.com/2bKlkcbe7h— Election Integrity Partnership (@2020Partnership) November 4, 2020
The Election Integrity Partnership said that one of them had come up as a top search result within YouTube when users searched election information in key swing states.
The research group estimated that more than 26,000 people had viewed the fake results.
YouTube said it that "after careful review" it was removing livestreams that broke its rules.
In a separate incident of apparent election interference, the FBI has said it is investigating a series of robocalls.
According to the Washington Post, an estimated 10 million automated calls were made over recent days telling people to "stay safe and stay home".
They did not specifically mention voting, and their origin remains unknown.