Some Palestinians celebrated the American attacks
Yasser Arafat is reported to have warned his people not to behave in a way that might give Israel an excuse to attack Palestinian areas, in the wake of the tragedies in America.
Palestinian legislator Dr Ziad Abu Amr says Mr Arafat fears Israel will wage a public relations campaign to tarnish the image of Arabs and Muslims, particularly Palestinians.
Dr Abu Amr says there is a risk to Palestinians that Israel will take advantage of the current emergency, using harsher tactics while America is preoccupied with its internal tragedy.
With wall-to-wall coverage of the attacks dominating regional and international media, the fact that nine Palestinians were killed overnight in the northern West Bank town of Jenin and another in the Gaza Strip, has barely registered.
Instead, images of Palestinians handing out sweets to celebrate what happened in the United States have dominated.
But Dr Abu Amr insists those responses do not reflect the general mood of Palestinian people.
He says many Palestinians have relatives in the United States and everyone was shocked and dismayed at the magnitude and gravity of the events in Washington and New York.
He cautions against premature judgments that someone from the Middle East is involved, but admits that if that is the case there will be very serious repercussions.