A recent US opinion poll showed as many as 49% of Republican male supporters did not want to get vaccinated.
Mr Trump last month said “everybody, go get your shot” at a conservative forum.
It was the first time he publicly encouraged Americans to do so. He has not commented on the issue since then.
Mr Trump, who was privately vaccinated in January, was absent when four other ex-presidents – Barack Obama, George W Bush, Bill Clinton and Jimmy Carter – appeared last week in a public service announcement for the vaccination.
The US is by the world’s worst-hit country by the pandemic, with more than 530,000 Covid-related deaths and nearly 29.5 million infections, according to Johns Hopkins University.
What did Dr Fauci say?
Dr Fauci, the chief medical adviser to President Joe Biden, told Fox News Sunday: “If he [Trump] came out and said ‘Go and get vaccinated, it’s really important for your health, the health of your family, and the health of the country’, it seems absolutely inevitable that the vast majority of people who are his followers would listen to him.
“He’s such a strongly popular person. I cannot imagine that if he comes out that they would not get vaccinated.”
Dr Fauci said the Trump administration was “very successful in getting us the vaccines we have right now”.
“It seems like an intrinsic contradiction, the fact that you have a programme that was started during his presidency, and he’s not out telling people to get vaccinated.
“I wish he would. He has such incredible influence over people in the Republican party – it would really be a game-changer if he did,” Dr Fauci said
The two were summoned to answer questions about how their platforms had limited distribution of a controversial article about Joe Biden’s son published ahead of the US election.
But they are also being challenged over their handling of posts by President Trump and others who have contested the vote’s result.
It says the platforms are generally not responsible for illegal or offensive things users post on them.
Mr Biden has said this allows them to spread “falsehoods they know to be false”.
Republicans have also voiced concern about the law. They claim it lets social media companies take decisions about what to leave up and take down without being transparent about why, making bias possible.
“When you have companies that have the power of governments, have more power than traditional media outlets, something has to give,” said the Republican Senator Lindsey Graham, who is chairman of the Senate Judiciary Committee.
image captionSenator Lindsey Graham warned the social networks that “change is going to come”
Facebook’s Mark Zuckerberg and Twitter’s Jack Dorsey both addressed the issue in their opening remarks.
Mr Dorsey urged the politicians to work with Twitter to avoid changes that might cause “the proliferation of frivolous lawsuits, and severe limitations on our collective responsibility to address harmful content”.
Mr Zuckerberg added that any update must preserve “the freedom for people to express themselves and for entrepreneurs to build new things”.
The two tech CEOs also defended their record in handling the 2020 election.
But Mr Dorsey acknowledged that Twitter’s decision to block links to the New York Post article about Hunter Biden had been “wrong”, and that its failure to subsequently restore the newspaper’s own tweets about the story had required a further policy change.
image captionMr Dorsey acknowledged that the way Twitter’s policies were enforced could be “opaque” to outsiders
“I hope this… demonstrates our ability to take feedback, admit mistakes and make all changes transparently to the public,” he said
Mr Zuckerberg avoided direct reference to the matter.
However, he used the opportunity to challenge recent claims by Democrats that Facebook had been slow in removing posts that promoted insurrection and violence.
“We strengthened our enforcement against militias and conspiracy networks like QAnon to prevent them from using our network to organise violence or civil unrest,” Mr Zuckerberg said.
The two tech leaders have been challenged over some of their recent decisions.
The Democratic Senator Richard Blumenthal wanted to know why Facebook had not banned Steve Bannon.
President Trump’s former top advisor recently called for the beheadings of disease expert Dr Anthony Fauci and the FBI director Christopher Wray in a video he posted to both Twitter and Facebook.
Twitter threw him off its service, but Facebook only froze Mr Bannon’s page.
Mr Zuckerberg said Mr Bannon “did violate our policies” but had not clocked up enough strikes to permanently lose access.
And when the senator called for a rethink, Mr Zuckerberg responded: “That’s not what our policies would suggest we should do.”
image captionMr Zuckerberg said he thought there was a role for regulation in Facebook’s use of algorithms
Mr Zuckerberg went on to dispute reports that Facebook had forgiven infractions by both of Donald Trump’s sons and the news site Breitbart, among others, in order to avoid accusations of bias from conservatives.
“Those reports mischaracterise the actions that we’ve taken,” he said.
The Democratic Senator Dianne Feinstein followed up with questions to both executives over their responses to President Trump’s posts about election fraud, which lacked factual basis.
She asked Twitter’s chief whether he thought adding labels but allowing the tweets to remain visible went far enough.
Mr Dorsey responded that he believed providing “context” and “connecting people to the larger conversation” was the right path to follow.
Senator Feinstein went on to ask Mr Zuckerberg if he felt enough had been done to prevent people delegitimising the election’s result given that hashtags for Steal The Vote and Voter Fraud had garnered more than 300,000 interactions on its platforms in the hours after Mr Trump falsely declared victory.
image captionSenator Feinstein questioned whether labels do enough to counter misinformation
“I believe we have taken some very significant steps in this area,” Mr Zuckerberg responded, pointing to information it had placed at the top of the screens of US-based Facebook and Instagram users.
“I think that we really went quite far in terms of helping to distribute reliable and accurate information about the results.”
Meanwhile, the Republican Senator Michael Lee brought up Twitter’s suspension of an account belonging to Mark Morgan, the commissioner of US Customs and Border Protection.
The action was taken after Mr Morgan tweeted that the wall on the border with Mexico had helped stop “gang members, murderers, sexual predators and drugs from entering our country”.
“What exactly is hateful about [that]?” asked Senator Lee.
Mr Dorsey acknowledged that the action had been taken in error.
“There was a mistake and it was due to the fact that we had heightened awareness around government accounts,” he explained.
The Senator responded: “I understand that mistakes happen, but what we’re going to see today is that mistakes happen… almost entirely on one side of the political aisle rather than the other
US President Donald Trump has completed his course of treatment for Covid-19 and can return to public engagements this weekend, his physician has said.
Dr Sean Conley said the president had responded “extremely well” to medication and had “remained stable”.
Mr Trump later said he would probably take another Covid test on Friday and hoped to hold a rally over the weekend.
Critics have accused the White House of avoiding questions about Mr Trump’s health and testing in recent days.
A White House spokeswoman said the president wanted to return to the campaign trail this weekend.
But an administration official later said Trump was unlikely to travel so soon because the logistics of organising events at short notice was problematic. An appearance is more likely on Monday, they said.
The president is also set to have a televised “medical evaluation” on Fox News on Friday evening.
Meanwhile, House Speaker Nancy Pelosi, the most powerful Democrat in Washington, on Friday announced legislation to establish a commission to assess a president’s fitness for office.
Mrs Pelosi said it was not meant to rule on Mr Trump’s condition, but any serious consideration of the measure is unlikely.
What’s this commission about?
Democrats are focusing on a clause in the 25th Amendment that allows a president to be removed from office against their will because of a physical or mental incapacity.
The amendment was introduced after the 1963 assassination of President John F Kennedy to clarify issues around the transfer of presidential powers. It can only be invoked if the vice-president and a majority of cabinet secretaries or Congress agree.
Democrats are looking to set up mechanisms that would enable Congress to have more say on a president’s fitness.
Conservatives say this is a political move to attack Mr Trump’s health ahead of the election.
On Friday, Mrs Pelosi said the move was “not about President Trump”, who “will face the judgment of the voters”.
“This legislation applies to future presidents but we are reminded of the necessity of action by the health of the current president.”
Previewing the legislation on Thursday, Mrs Pelosi told reporters that serious questions concerning Mr Trump’s health were still unanswered, and described the president as being in an “altered state”.
Mr Trump called Ms Pelosi “crazy” and said she was “the one who should be under observation”.
What’s the latest on Trump’s health?
Speaking on Fox News late on Thursday, Mr Trump said he was feeling “really good” and hoped to hold a campaign rally on Saturday evening, possibly in Florida.
The president was also heard clearing his throat and coughing during the interview. At one point, he appeared to mute his mic after needing to clear his throat.
Fox News has since said that Mr Trump will appear for a televised “medical evaluation” on Friday at 20:00ET (01:00BST). It will be his first on-camera interview since his diagnosis and he will undergo an evaluation by Dr Mark Siegel, a Fox contributor.
Earlier this week, White House doctor Dr Conley had said that if the president’s condition remained the same or improved throughout the weekend and into Monday, “we will all take that final, deep sigh of relief”.
Although the names of many people who have interacted with the president and tested positive are now known, it remains unclear just how many were exposed at the White House. New Covid safety measures are in place there.
One of the top Republicans, Senate majority leader Mitch McConnell, said on Thursday that he had not been to the White House since 6 August because its approach to handling Covid with social distancing and masks was “different from mine and what I suggested we do in the Senate”.
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