MONTEZUMA, Iowa — Attorneys in the case of a Mexican man accused of killing an Iowa college student sparred Wednesday over the suspect’s immigration status, and a defense lawyer lashed out at President Donald Trump for suggesting that his client is guilty in comments that he said would “poison” the entire jury pool.

So far, prosecutors are standing by their allegations that Cristhian Bahena Rivera, 24, was in the country illegally when he abducted and killed Mollie Tibbetts, a 20-year-old student whose body was found Tuesday. Prosecutors have charged Rivera with first-degree murder, and he’s being held on a $5 million bond.

But Rivera’s lawyer filed paperwork arguing that Rivera had legal status to be in the country, and he referred to comments by an employer that believed Rivera was able to work at a nearby dairy. In the documents, defense attorney Allan M. Richards noted Trump’s use of the case to rail against the nation’s immigration system.

“Sad and Sorry Trump has weighed in on this matter in national media, which will poison the entire possible pool of jury members,” Richards wrote.

Prosecutors did not directly address the defense claim other than to note after the hearing their understanding that Rivera was in the country illegally.

Shortly after his arrest, investigators stated that Rivera did not have legal status, and Immigration and Customs Enforcement officials lodged an immigration detainer for Rivera, a move that means the agency has probable cause to believe he is subject to deportation.

On Tuesday night, the owners of the dairy farm said they had confirmed Rivera’s immigration status with an E-Verify electronic status check. But on Wednesday, the dairy owners said Rivera was hired under a different name after presenting an out-of-state photo identification and a matching Social Security card.

The employer, Yarrabee Farms, ran it through a Social Security verification system.

Richards claimed his client “has the legal documents” to work in the U.S. He said his client was recruited to work at a local farm, passed government vetting and has worked and paid taxes for years. He acknowledged his client’s status may be a “matter of interpretation.”

The defense sought a gag order due to Trump’s comments. Magistrate Judge Diane Crookham-Johnson said she would consider the request. Richards also asked that the proceedings be closed. The judge denied that request.

Rivera has allegedly confessed to the killing. Trump seized on his arrest on Tuesday to call the nation’s immigration laws “a disgrace” that will only be fixed by electing more Republicans.

Iowa’s Republican governor, facing a tough re-election challenge in November, blasted an immigration system that “allowed a predator like this to live in our community.” And Iowa’s two GOP senators called the death a tragedy that “could have been prevented.”

Rivera led investigators early Tuesday to a body believed to be Tibbetts in a cornfield about 12 miles southeast of Brooklyn, Iowa, where she was last seen going for an evening run, Iowa Division of Criminal Investigation special agent Rick Rahn said.

Authorities did not offer a motive.

Within hours, Trump noted the arrest at a rally in West Virginia.

“You heard about today with the illegal alien coming in, very sadly, from Mexico and you saw what happened to that incredible, beautiful young woman,” Trump told the crowd in Charleston. “Should’ve never happened. Illegally in our country. We’ve had a huge impact, but the laws are so bad. The immigration laws are such a disgrace. We’re getting them changed, but we have to get more Republicans. We have to get ‘em.”

Iowa Gov. Kim Reynolds said residents were heartbroken and angry. Sens. Chuck Grassley and Joni Ernst vowed that they “cannot allow these tragedies to continue.”

Trump has made cracking down on illegal immigration a core policy of his administration. He often has claimed widespread crime by people living in the country illegally, citing among other things the indictments of 11 suspected MS-13 gang members from El Salvador charged in connection with the slayings of two Virginia teens. Trump also has held events at the White House with members of “angel families,” whose relatives were killed by immigrants.

Although Trump claims legal U.S. residents are less likely to commit crime, several studies from social scientists and the libertarian think tank Cato Institute have concluded that isn’t accurate and that states with a higher share of people living in the country illegally have lower violent crime rates.

Investigators said they believed Rivera had lived in the area from four to seven years.

In a statement late Tuesday, Yarrabee Farms said Rivera had worked at its farms for the last four years and was an employee in good standing. The Brooklyn-based company said it was shocked to hear that Rivera was charged in Tibbetts’ death. Yarrabee Farms is owned by the family of Craig Lang, a prominent Republican who previously served as president of the Iowa Farm Bureau.

A search of Iowa court records revealed no prior criminal history, and it’s unclear whether he had ever been subject to prior deportation proceedings.

Rivera’s Facebook page described him as being from Guayabillo, a community of less than 500 people in the Mexican state of Guerrero. It’s about a three-hour drive from the resort city of Acapulco.

Investigators said they zeroed in on Rivera after obtaining footage from surveillance cameras in Brooklyn. The footage showed a Chevy Malibu connected to Rivera that was driving back and forth as Tibbetts was running in the area, Rahn said.

A conviction on first-degree murder carries a mandatory sentence of life in prison without parole in Iowa, which does not have the death penalty.

Tibbetts would have started her junior year at the University of Iowa, where she was a psychology major.