Sami Esmail, a Brooklyn-born American citizen of Palestinian descent, flew into Tel Aviv's Ben Gurion Airport last Dec. 21 to see his dying father on the Israeli-occupied West Bank. He was promptly arrested by Israeli police on charges he belonged to an extremist Palestinian organization and had been trained as a terrorist.

Esmail, 24, is still in an Israeli jail, and his supporters fanned across Washington recently seeking congressional and other official help to get him freed.

He was tried under an Israeli law that makes it a crime to belong to an "illegal organization" - in his case the Popular Front for the Liberation of Palestine.

He was accused of joining the groupat Michigan State University, where he is an electrical engineering student, and of having "contact with an enemy agent" during a visit to Libya in the summer of 1976. He was accused of undergoing PFLP military training in Libya then.

The verdict of a three-judge panel is due June 7.

The case has aroused great interest in America's Arab community and among Esmail's professors and classmates at Michigan State - many of who have taken little interest in political causes and, until now, in Mideast affairs.

At one point, Sen. James Abourezk (D-S.D.), threatened to filibuster against the nomination of Benjamin R. Civiletti to be deputy attorney general until he received answerson the FBI's role in the case. Even the Detroit City Council, with a large Arab population among its constituents, passed a resolution supporting Esmail.

Esmail's supporters, who include a number of American Jews, argue that he confessed after six days of harsh questioning during which he was not allowed a full night's sleep, was pushed around, threatened with not being able to see his dying father and kept from seeing his lawyer.

His supporters also deny that he underwent military or terrorist training in Libya and said he only took a free trip there out of curiosity about the country and to seek about getting a university job there.

Israel, in a series of statements relased through its embassy here, defended the arrest as necessary to protect the country from terroist attacks and denied that Esmail had been mistreated in jail.

It called much of the information sent out by the National Committee to Defend the Human Rights of Sami Esmail, "tendentious and misleading . . . clearly designed to subvert the cause of justice and draw attention away from the serious nature of the charges and is intended to present both Israel and its legal system in an negative and oppressive light."

State Department officials, though, said that Esmail told an American vice consul that he had been mistreated before signing the confession. The State Department said it had no reason to doubt Esmail's story then, and had asked Israel to investigate.

Two American law professors well known for their civil liberterian views - Monroe H. Freedman of Hofstra and Alan Dershowitz of Harvard - witnessed the trial and thought it was fair.

But both thought Esmail's confession - the main Israeli evidence against him - should not have been accepted by the court because he had been held too long without being able to see his lawyer - Felecia Langer, an Israeli Jew well known for defending Palestinians.

Esmail's supporters said Israel learned of his trip to Libya from the FBI, whose agents questioned him on his return. Although the FBI acknowledged sending some information about Esmail to Israel, it told Senate aides that it got more information back than it gave.

It was the FBI's role and the laws under which he was arrested that aroused the ire of Abourezk, the pricipal pro-Arab spokeman in the Senate and Rep. M. Robert Carr (D-Mich.), a former civil rights lawyer.

"First of all," said Abourezk, "he committed no crime in Israel at all. And even if he had been training under the PFLP, which I don't believe, and he became an indesirable character, the answer is to turn him away, not arrest and torture him. That's what the U.S. does. We turn them away, not arrest them."

Lawyers, however, agree that Israel has a right under international law to arrest people for crimes affecting it but not committed within its borders. It is done by the United States, for example, in antitrust cases involving international cartels and in narcotics cases.