Nearly 1,800 people signed a letter calling on him to release documents that they believe implicate officials from Saudi Arabia in the plot.
They say that if he refuses, he should not attend ceremonies next month to commemorate the 20th anniversary.
Nearly 3,000 people died on 9/11.
The attacks were committed by the Al Qaeda terror group, investigators say, and triggered the US invasion of Afghanistan. Fifteen of the 19 plane hijackers were Saudi nationals.
“We cannot in good faith, and with veneration to those lost, sick, and injured, welcome the president to our hallowed grounds until he fulfils his commitment,” says the letter from family members, first responders and survivors.
They call on President Biden to stay away from the three sites where the attacks took place – in New York, Virginia and Pennsylvania.
The families have long argued that Saudi officials had advance knowledge of the attack, and did nothing to stop it. They have sued the government of Saudi Arabia, which has denied being involved.
Last month, the lawsuit saw several top former Saudi officials questioned under oath. The depositions remain sealed, further upsetting families.
“Since the conclusion of the 9/11 Commission in 2004 much investigative evidence has been uncovered implicating Saudi government officials in supporting the attacks,” the families’ statement continues.
“Through multiple administrations, the Department of Justice and the FBI have actively sought to keep this information secret and prevent the American people from learning the full truth about the 9/11 attacks.”
The administrations of George W Bush, Barack Obama and Donald Trump also declined to declassify the documents, citing national security concerns.
“Twenty years later, there is simply no reason – unmerited claims of ‘national security’ or otherwise – to keep this information secret,” the group writes. “But if President Biden reneges on his commitment and sides with the Saudi government, we would be compelled to publicly stand in objection to any participation by his administration in any memorial ceremony of 9/11.”