A Newark federal judge on Friday heard arguments on whether the case to free Mahmoud Khalil, a leader of pro-Palestinian protests at Columbia University, should continue to play out in New Jersey or be transferred to Louisiana, a potentially more favorable venue for the government’s case.

The judge, Michael Farbiarz, did not make an immediate decision, but is expected to rule soon. Mr. Khalil, a legal permanent resident, was detained on March 8 at his New York City apartment, sent briefly to a New Jersey detention center and now has been held for nearly three weeks in a facility in Jena, La.

While Mr. Khalil’s lawyers are fighting for his freedom, the Trump administration is seeking to deport him, saying that he spread antisemitism through his involvement in the protests. If Mr. Khalil stays in Louisiana, his case could end up in one of America’s most conservative appeals courts. Those judges could decide whether the government’s rationale for detaining Mr. Khalil could be used in other cases.

The case was originally filed in New York, but a judge there decided he lacked jurisdiction and that it should be heard in New Jersey. The attempts by Mr. Khalil’s lawyers to free him have created a tangle of litigation, much of which has focused on a seemingly technical question: In which court should his case be heard?

On Friday in Newark, Baher Azmy, a lawyer for Mr. Khalil and legal director of the Center for Constitutional Rights, argued in court that transferring the case to Louisiana would set a precedent for other activists to be moved without legal justification, which he called “Kafkaesque.”

The government’s case against Mr. Khalil was undertaken “in order to retaliate against constitutionally protected speech,” Mr. Azmy said.

But a lawyer for the government, August E. Flentje, said it “made no good sense” for the case to be heard in New Jersey when Mr. Khalil had been arrested in New York, asserting that “the case belongs in Louisiana.”

Judge Farbiarz delayed ruling on a request from Mr. Khalil’s lawyers that he be granted bail, saying he first wanted to resolve the issue of where the case would be heard.

Mr. Khalil is one of at least nine protest participants who have been arrested and detained this month. Unlike some others, he is a legal resident, married to an American citizen who is expected to give birth next month.

He has not been charged with a crime. Instead, the secretary of state, Marco Rubio, has cited a rarely used law to explain Mr. Khalil’s detention, saying that the recent graduate threatens the Trump administration’s foreign policy goal of halting the spread of antisemitism.

Mr. Khalil’s lawyers initially asked for his release in New York federal court. But the judge there determined that it should be heard neither there, nor in Louisiana, but in New Jersey, where Mr. Khalil was being held at the moment his lawyers filed court papers. Accordingly, the case itself was transferred to New Jersey last week.

Once there, the government’s lawyers continued to fight to transfer the case to Louisiana. In a filing, they noted that Mr. Khalil had never filed a petition in New Jersey — and argued that the court had no jurisdiction.

The administration has reason to continue its fight. If the legal battle is waged in Louisiana, it is likely to make its way to the U.S. Court of Appeals for the Fifth Circuit, which from New Orleans presides over cases from that state.

The Fifth Circuit is known as one of the country’s most conservative, and in the past has sided with government officials over noncitizens. If its judges rule in favor of the Trump administration, Secretary Rubio could continue to cite the law used to justify the detention of Mr. Khalil in efforts to deport other legal permanent residents.

Friday’s hearing came days after a judge in Manhattan ordered the government to halt efforts to detain Yunseo Chung, a 21-year-old Columbia student and legal permanent resident who had participated in pro-Palestinian protests. Ms. Chung, who shares a legal team with Mr. Khalil, was never detained by immigration authorities.

In an interview outside the courthouse after the hearing, Mr. Azmy noted the distinction between her case and Mr. Khalil’s.

“The fact that he’s in custody allows the government to have total control over him,” Mr. Azmy said.

As the hearing played out, around 50 demonstrators assembled outside the Newark courthouse to protest Mr. Khalil’s detention. They waved Palestinian flags, held signs and chanted.

“Hands off our students! ICE off our campus!” read one sign. “Opposing genocide does not mean supporting terrorism.”

Speaking at the rally, Amy Torres, executive director for the New Jersey Alliance for Immigrant Justice, pointed to a chilling effect on free speech created by the detention of students across the country.

“They have only targeted people that they view to be voiceless,” she said, adding, “This is about this administration taking the issue that they believe is the least sympathetic, and making an example out of the people that they arrest.”

Jonah E. Bromwich contributed reporting.