"Whatever is going on in the Middle East ... people in New York have a right to have very strong feelings about it," Giuliani said. "But they have no right to harm anyone else, to harm anyone else physically, or to harm their property."
Over the past three days in Brooklyn, where large numbers of the city's Jewish and Arab populations live, a bus for Jewish schoolchildren has been burned and a Jewish man has been accosted on the street and slashed with a knife.
"We want to make certain that everyone understands the line, the line that has to be drawn, and the New York City Police Department is prepared to and has and will arrest anyone who violates the law," Giuliani said.
After a meeting at City Hall, dozens of representatives of Jewish and Arab groups told a news conference about their "commonality" and "unity" as New Yorkers who want to prevent the crisis between Israel and the Palestinians from spilling onto city streets.
At least 60 people have been killed and more than 1,000 injured in six days of violence in Gaza and the West Bank.
Israeli Prime Minister Ehud Barak and Palestinian Authority President Yasser Arafat agreed in Paris on Wednesday night to an accord to end the violence in the West Bank and other areas, U.S. and Israeli sources said late Wednesday.
Under the draft accord, Israeli army forces and Palestinian security forces would pull back from trouble spots. But one Palestinian source disputed that account, and there were discrepancies about how much progress had been made.
Police hope to control rumors
New York Police Commissioner Bernard Kerik said at the same City Hall news conference that police were investigating 10 incidents possibly related to bias. No arrests have been made.
Kerik said "our concern is more rumor control than anything else." For example, he said that after a Jewish youth cut his hand on a soda can, a false story quickly spread through the community that he had been stabbed.
Describing the overall situation as "relatively benign," Kerik nevertheless said police officers would be placed on duty at mosques and synagogues, and he ordered the deployment of more officers in Jewish and Arab neighborhoods.
Emira Habibi-Browne of the Arab-American Family Support Council told reporters that it was not well known that her group and others had worked "very closely" with Jewish organizations over the years.
"Unfortunately we are very stereotyped," she said. "We need to hear both sides of the story because emotions are running extremely high right now and we cannot but expect a spillover.
"But the immigrants who come here, come here because this is a wonderful city and a wonderful country with freedoms, and they want to express themselves. But they should do it in a legal way," Habibi-Browne said.
Michael Nussbaum, president of the American Jewish Congress for the New York region, said Wednesday's gathering "demonstrates that the leaders of our communities are willing to work for the unity of New York, and it is also important that the children of the city as well as the adults understand that there is a message that needs to be explained to them."
Giuliani, who received strong support from conservative Jewish voters in winning two four-year terms as mayor, said the various groups were working together to release a joint statement on Thursday.
CNN Chief International Correspondent Christiane Amanpour and Reuters contributed to this report.