President Donald Trump with former President Barack Obama and former Vice President Joe Biden after being sworn in as president on January 20, 2017, at the US Capitol. MARK RALSTON/AFP/Getty Images

Hours after Joe Biden formally launched his bid for the presidency on Thursday, President Donald Trump described him on Twitter as "sleepy" and questioned the former vice president's intelligence.

The president's attacks, however, reportedly mask concern that Biden could defeat him in 2020.

Biden visited Pennsylvania on Thursday, a swing state viewed as crucial to Trump's reelection.

A poll Wednesday found Biden with an 8-point lead over Trump in a head-to-head contest.

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Hours after Joe Biden formally launched his bid for the presidency on Thursday, President Donald Trump greeted the news in characteristic fashion - with a series of personal insults about the former vice president.

"Welcome to the race Sleepy Joe," Trump tweeted. "I only hope you have the intelligence, long in doubt, to wage a successful primary campaign.

"It will be nasty - you will be dealing with people who truly have some very sick & demented ideas. But if you make it, I will see you at the Starting Gate!"

In Biden's video announcing his candidacy, he framed the prospect of four more years of a Trump presidency as a threat to US democracy, seizing on images of white nationalists - whom Trump did not unequivocally condemn -marching in Charlottesville, Virginia, in August 2017.

A scene from Biden's announcement video of white supremacists protesting in Charlottesville, Virginia. Joe Biden

Trump resumed his attacks later in an interview with Fox News' Sean Hannity, saying he had been urged to smear Biden with another word that rhymes with "sleepy" (an allusion to the "creepy Joe Biden" memes that play on some women's accusations of inappropriate touching).

Trump said he ultimately decided the strategy was "too nasty," continuing the unwelcome optics of seeming to sympathize with Biden over issues having to do with the treatment of women.

The president's attacks, though, reportedly mask an underlying fear that Biden is the Democrat best placed to defeat him in 2020.

A Republican strategist said to have direct knowledge of events in the White House told Politico on Thursday that the president had been discussing the threat Biden posed for months.

"How are we gonna beat Biden?" the president would reportedly ask, apparently not reassured even when aides suggested Biden wouldn't defeat his more left-leaning competition in the Democratic primaries.

The source of Trump's concern is the Democrat's credibility in the Rust Belt swing states of Wisconsin, Michigan, and Pennsylvania - which Trump took from the Democrats in 2016 after promising a renewal of blue-collar manufacturing jobs.

A source of particular concern is Pennsylvania, which, despite his long stint as a US senator for Delaware, is Biden's home state.

A Republican who has attended meetings with Trump told CNN on Thursday that Trump frequently asked about Biden's strength there.

Biden visited Pennsylvania on the first day of his presidential campaign, heading to a fundraiser held by David L. Cohen, the executive senior vice president of Comcast. He is expected to make his first major stump speech as a presidential candidate on Monday in Pittsburgh.

The president earlier retweeted a message by the Republican Party chair, Ronna McDaniel, highlighting the administration's economic record in the state.

"Biden chose Pennsylvania to launch his campaign - a state where the unemployment rate just dropped to the lowest level *ever recorded*," she tweeted.

National polls seem to bear out the president's concern, with a Politico/Morning Consult poll last weekend of registered voters showing Biden with an 8-point lead over Trump in a head-to-head contest.

Analysts, though, are skeptical about whether Biden, at 76, can command the support of the party's young, left-leaning, energized base in seeking the Democratic nomination.

He continues to be face questions about whether he is out of step with the values of the party.

One damaging example was Anita Hill telling The New York Times on Wednesday that she did not accept Biden's recent apology for his handling of Clarence Thomas' 1991 Supreme Court confirmation hearings, in which she accused Thomas of sexual harassment.

Biden on Thursday refused to be drawn in to exchanging insults with the president, remarking to reporters in Delaware when told of Trump's tweet, "Everybody knows Donald Trump."

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