Nearly 1800 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 3000 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.
