The former VP spoke to the camera in a video that included scenes of civil rights struggles and protests, both past and present, as the country marks the national holiday amid nationwide calls for an end to police brutality and systemic racism.
He said: “Our country was founded on an idea: ‘We hold these truths to be self-evident, that all men are created equal.’ We’ve never lived up to it. Jefferson himself didn’t – he held slaves, women were excluded. But once proposed, it was an idea that couldn’t be restrained.
“Through it all, these words have gnawed at our conscience and pulled us towards justice."
Mr Biden referenced America's ugly history of racism, the assassination of Dr Martin Luther King Jr and the killing of George Floyd by Minneapolis cops in May, and called on the country to live up to the words that founded the nation.
"We have a chance now to give the marginalized, the demonized, the isolated, the oppressed, a full share of the American dream. We have a chance to rip the roots of systemic racism out of this country," he said.
The Democrat nominee's video message did not mention the president but came hours after Mr Trump dug deeper into the divisiveness that was wrought the country by accusing protesters who have pushed for racial justice of engaging in a “merciless campaign to wipe out our history".
At the foot of Mount Rushmore, on the eve of Independence Day, Mr Trump struck a discordant tone to an electorate battered by a pandemic and seared by the recent high-profile killings of black people.
He zeroed in on the desecration by some demonstrators of monuments and statues across the country that honour those who have benefited from slavery, including some past presidents.
Four months out from the election, Mr Trump's comments amounted to a direct appeal to the political base, including many disaffected white votes, that carried him to the White House in 2016.
“This movement is openly attacking the legacies of every person on Mount Rushmore,” Trump said.
He lamented “cancel culture” and charged that some on the political left hope to “defame our heroes, erase our values and indoctrinate our children.” He said Americans should speak proudly of their heritage and shouldn’t have to apologise for its history.
“We will not be terrorized, we will not be demeaned, and we will not be intimidated by bad, evil people,” Trump added. “It will not happen.”
On Saturday, Mr Biden is scheduled to attend the Essence Festival of Culture to hear from black women while Mr Trump will host a "Salute to America" event in DC.
AP contributed to this report