The suspect, Ghazi Ibrahim Abu Maizar, stated in his asylum application that Israeli soldiers had tortured him and falsely accused him of being a member of the militant Islamic group Hamas, and he was free on $5,000 bond this spring and summer while his asylum request was pending.

Mr. Giuliani has sharply criticized immigration officials and judges for not insisting that Mr. Abu Maizar be detained until they had investigated whether he was a member of Hamas. The Mayor pointedly noted that Israel is an important American ally.

Mr. Giuliani and Senator Alfonse M. D'Amato said at a City Hall news conference yesterday that they were sending a joint letter to the I.N.S. Commissioner, Doris Meissner.

''We believe it's very, very important that we get answers as to what happened with regard to some of the people who were allowed to come into New York City,'' Mr. Giuliani said.

''How did it happen, why did it happen, and what can be done to protect people more effectively in the future?''

But Federal officials yesterday defended their handling of his case, saying that Mr. Giuliani did not understand the laws and international conventions that govern the treatment of refugees and asylum seekers. A person's nationality is not relevant in an asylum case, they said.

''The Mayor of New York is an attorney,'' said Richard Kenney, a spokesman for the executive office for immigration review, the branch of the Justice Department that operates the immigration courts. ''He should read the law.''

In one New York case earlier this year, a former member of the Irish Republican Army who had been convicted on a terrorist charge was granted asylum in the United States. He was not detained while his asylum case was pending.

Immigration authorities appealed the judge's grant of asylum to the man, Brian Desmond Pearson, in part because they considered him a convicted terrorist.

In Mr. Abu Maizar's case, Federal officials note that there was no evidence at that time that he was a member of Hamas. Nor has an intensive investigation since his arrest in Brooklyn on Thursday turned up any such evidence yet. His statement in an application that he had been wrongly accused of being part of a terrorist group would not have set off a law enforcement investigation, they said.

Rather, the immigration judge and lawyers for the Immigration and Naturalization Service would have studied the statements and other evidence to determine whether he had a legitimate basis for seeking protection in the United States. In Mr. Abu Maizar's case, for example, officials might have asked the State Department and even the Israeli Government about the Hamas question, but only in the context of figuring out whether he should be given asylum.

''Remember, the asylum claim is just that, a claim,'' said Russell A. Bergeron Jr., a spokesman for the Immigration and Naturalization Service. ''It is not evidence.''

Mr. Abu Maizar's statement would not have been immediately assumed to be implausible since ''terrorism is in the eye of the beholder,'' Mr. Bergeron said. ''Are our critics saying that everyone arrested in the Gaza Strip over the past decade was a terrorist?''

Immigration officials stress that the asylum process is both confidential and separate from law enforcement. The reason, they said, is simple: If people who had been tortured or persecuted in their native countries fear that their statements about their government could be used against them or their families back home, they would be afraid to come forward and ask for refuge. And their nationality would be irrelevant to their eligibility to ask for asylum.

''The law is meant to provide protection to individuals subject to persecution in their home country,'' Mr. Kenney said. ''It does not matter if the person is from a democratic country or a totalitarian country or something in between.''

''Enforcement is not an issue in asylum cases, period,'' he said. ''We don't use an asylum application to determine if someone is a danger.''

To strengthen the separation between the asylum process and law enforcement, the division of the Immigration and Naturalization Service that represents the Government in asylum claims is independent from the district directors, who oversee law enforcement investigations.

When Mr. Abu Maizar was caught by Border Patrol officers in January after he had illegally entered the country from Canada into Washington State, his was just a simple deportation case. The immigration service held him on a $15,000 bond, which a judge in Seattle, Anna Ho, reduced to $5,000 on Feb. 6.

Mr. Abu Maizar was released on bond, while the Government tried to deport him to another country. Canada had refused to take him back.

''At that point he was just an illegal alien,'' Mr. Kenney said.

But on April 7, Mr. Abu Maizar filed his asylum application with the court. Judge Ho had no hearing date available for nine months, so the case was transferred to another immigration judge in Seattle, Kendall Warren, who scheduled a hearing for June 23. At that hearing, Mr. Abu Maizar withdrew his asylum application and agreed to leave the United States within 60 days.

''In this case, there is no reason or evidence to indicate he should ever have been held,'' Mr. Kenney said. ''The Mayor is seeing all this in hindsight.''