As a student at the University of Florida, Lara Alqasem served a recent stint as president of the tiny local chapter of Students for Justice in Palestine.
The group typically had a single-digit membership, and one of its more notable political activities appears to have been a campaign to boycott an Israeli brand of hummus. A Facebook event post indicated that all of 19 people showed up for the campaign’s launch.
But that seems to have been enough for the Israeli government to bar Ms. Alqasem from entering the country under a 2017 law intended to combat the boycott, divestment and sanctions movement, a loose network whose goals include pressuring Israel into ending the occupation of the West Bank. Israeli officials consider the B.D.S. movement to be anti-Semitic and bent on Israel’s destruction, since it also promotes the right of return for millions of Palestinian refugees to their former homes.
Ms. Alqasem arrived at Ben Gurion Airport last week with plans to enroll at an Israeli university, and has been held there since while she appeals a deportation order. On Tuesday, the Israeli government presented her with a choice: Apologize and renounce her support for the boycott movement, or give up on her plan to study in Israel and be placed on a plane back to the United States.
“If Lara Alqasem declares clearly and explicitly that she erred in the past,” Gilad Erdan, Israel’s minister for public security and strategic affairs, wrote on Twitter, “we will reconsider our position regarding her entry to Israel.”
One of the Israeli lawyers representing Ms. Alqasem, Leora Bechor, described the case as “egregious.”
“This is a 22-year-old who definitely cannot be in support of an academic boycott,” Ms. Bechor said. “She wants to study here.”
Amid a heated internal debate over the character of Israeli democracy, and who should be allowed into the country, Ms. Alqasem’s case has been testing the system. Her supporters accuse the government of an overzealous border policy that is based on flimsy evidence and is likely to do more damage to Israel and its image abroad than any student’s boycott call.
Ms. Alqasem’s credentials as an anti-Israel activist are far from clear-cut.
While at the University of Florida, she studied Hebrew and was spotted at a Holocaust survivor’s lecture, according to her Hebrew teacher, who wrote to Haaretz to attest to Ms. Alqasem’s character after reading an article about her ban.
After graduating, Ms. Alqasem, who has Palestinian grandparents, decided to study for a master’s in human rights law at the Hebrew University of Jerusalem. She landed on the night of Oct. 2 with a one-year student visa issued by the Israeli Consulate in Miami.
In an extraordinary step, the Hebrew University has asked to join Ms. Alqasem’s legal appeal against deportation.
“To be clear, we strongly oppose the boycott campaign against Israel, and Israel has to fight it,” Barak Medina, the rector of Hebrew University, said by telephone on Tuesday. “But to deny entry to every person who has expressed support for a boycott is counterproductive.”
Professor Medina said that he had not been able to meet Ms. Alqasem yet, but that he would like to.
Ms. Alqasem’s former Hebrew teacher, Dror Abend-David, described her as “a delightful young woman, an outstanding student, curious, with an open mind, and someone who very much wanted to study international relations in Israel to develop her own opinion on the conflict.”
Mr. Erdan, the public security minister, said that Ms. Alqasem was not being detained against her will and that she was free to leave the country anytime.
Critics are increasingly asking what the exact criteria are for barring people from the country. In the past, Israeli officials have said the 2017 entry law would not penalize people for their political opinions alone, and would apply only to major figures in the boycott movement.
While the law has so far been used sparingly — only about 15 people have been denied entry so far, according to officials — Israel has come under unwelcome scrutiny for detaining and questioning some high-profile critics at its entry points.
After arriving and being denied entry, Ms. Alqasem appealed to a tribunal at the Tel Aviv district court. At the request of a judge, she formally declared that she would not participate in any boycott activities while in Israel and that she had no intention of visiting the Palestinian territories, according to her lawyers, Ms. Bechor and Yotam Ben-Hillel.
The appeal was rejected, but Ms. Alqasem was granted an extension so that she could pursue her case further. Another hearing is set for the coming days.
Ms. Bechor said there was no evidence directly linking Ms. Alqasem to anti-Israeli activity.
The government’s file on Ms. Alqasem, she said, included no independent research and was based mostly on her profile on the website of an organization called the Canary Mission, which says it “documents people and groups that promote hatred of the U.S.A., Israel and Jews on North American college campuses.” The profile reports the activities of the Students for Justice in Palestine’s Florida chapter, but not of Ms. Alqasem herself.
Ms. Bechor said the government was now engaged in a “frantic effort to back down.”
Ben Moore, an adviser to Mr. Erdan, acknowledged that the ministry’s information about Ms. Alqasem came from public sources online, including the Canary Mission. He said Ms. Alqasem had deleted her social media accounts before coming to Israel, which he said “seemed dubious at best.”
By late Tuesday, it appeared that both sides were trying to find a compromise, in the wording of a statement, that would allow Ms. Alqasem to stay.