President Bush on the telephone to New York's
mayor
"We must be mindful that, as we seek to win the war, we treat Arab-Americans with the respect they deserve," Mr Bush said.
"There are thousands of Arab-Americans who live in New York City who love their flag," the president said. "We should not hold one who is a Muslim responsible for an act of terror."
He was speaking on the telephone to New York Mayor Rudolph Giuliani and New York State Governor George Pataki.
Violence
His warning comes after reports of violence against mosques and Arab-Americans.
In Chicago, police turned back some 300 people as they marched on a mosque in the southwest of the city.
Three of the demonstrators were arrested.
Also in Chicago, a firebomb was reported to have been thrown at an Arab-American community centre.
In Texas, shots were fired at another mosque, while Arab-American groups in several US cities say they have received death threats by phone, and hate messages on internet sites.
In New York, Mayor Giuliani has promised police protection for neighbourhoods with large numbers of Arab-Americans.
Mosques and Islamic centres in other cities were placed under 24-hour police guard.
Double tragedy
President of the Arab American Institute Dr James Zogby told BBC News Online it had been a trauma for all Americans, including Arab-Americans, many of whom had lost friends and relatives in the disaster.
"Arab-Americans are as afraid, grieving and mourning as everyone else.
But for us it's a double tragedy, because while we grieve, we're forced to look
over our shoulder."
Dr Zogby said he had received several death threats and was arranging security for his office.
"I take such threats seriously since my office was fire-bombed in 1980," he said.
Pearl Harbour
"Regardless of who is ultimately found to be responsible for these terrorist murders, no ethnic or religious community should be treated as suspect and collectively blamed," the Arab American Institute, based in Washington, said.
The chairman of the Arab-American Business and Professional Association in Washington, Fuad Sahouri, drew a parallel with what happened to Japanese-Americans in the wake of the attack on Pearl Harbour, to which Tuesday's attacks have been frequently compared.
"We don't want to be excluded or insulated or treated how Japanese-Americans were treated," he said.
"It's very important right now for Arab-Americans that their loyalty never be brought into question.
"We are Americans first."
Arab roots
There are thought to be around 3m US inhabitants who have roots in the Arab world.
Of these, the largest community is in Los Angeles, but the most influential group live in the Detroit and Dearborn area of Michigan, where about 300,000 Muslims live.
Arab-Americans are thought to have voted heavily in favour of Mr Bush in the presidential election.
Their most prominent political representative is the former Republican senator for Michigan, Spencer Abraham.
Mr Abraham is now President Bush's Energy Secretary.