(CNN) After an undocumented immigrant was arrested Tuesday in the presumed death of Mollie Tibbetts , President Donald Trump and other Republican lawmakers blamed the tragedy on the nation's immigration laws.

Cristhian Bahena Rivera, 24, is being held on a first-degree murder charge in the case of Tibbetts, a 20-year-old University of Iowa college student who was last seen jogging in Brooklyn, east of Des Moines, more than five weeks ago.

He faces life in prison without parole if convicted.

Rivera told police he followed Tibbetts with his car and pursued her when she started running away, said Rick Rahn, special agent in charge at the Iowa Division of Criminal Investigation.

Rivera is an undocumented immigrant from Mexico, according to US Immigration and Customs Enforcement. The agency sent a detainer request for Rivera to local authorities Tuesday, said Shawn Neudauer, an ICE spokesman.

Rahn said the suspect's motive is unclear.

"I can just tell you it seems that he followed her and seemed to be drawn to her on that particular day and for whatever reason, he chose to abduct her."

Suspect worked on farm owned by prominent Republican

Rivera has been in the area for four to seven years, Rahn said.

He had worked four years at an Iowa dairy farm based on false identification, his employer said Wednesday.

The farm where he was employed is owned in part by Craig Lang, a prominent Iowa Republican who ran for state secretary of agriculture this summer.

"We are still shocked to learn one of our employees was involved," he said in a statement expressing condolences to Tibbetts' family.

"We continue to cooperate with the investigation, and we have provided information about our former employee, including his hiring records, to authorities," Craig Lang's statement said. "There will be plenty of time later to discuss immigration. However, now is not that time. Now is a time to grieve and to remember Mollie."

Rivera was an employee in good standing who came to work on time and got along with his coworkers, said Dane Lang, the co-owner and manager of Yarrabee Farms.

"What we learned in the last 24 hours is that our employee was not who he said he was," he said.

In applying for the job, Rivera provided a state ID and social security card that was verified through the Social Security Administration's verification system, said Lang. But those forms of ID were not of Rivera, he said.

Rivera was not verified through E-verify, a system that is used by the US Citizenship and Immigration Services that verifies an immigrant's status in the US, but only through the Social Security number verification services, Dane Lang said.

Authorities have visited the farm and talked to employees, and the farm is cooperating with the investigation.

Trump calls immigration laws 'a disgrace'

Hours after the arrest was announced, the case started to emerge as yet another rallying point for Republican lawmakers and others who advocate for more restrictive immigration laws.

At a rally in Charleston, West Virginia, President Trump referred to Tibbetts' death -- which hasn't officially been confirmed -- and called the nation's immigration laws "a disgrace."

"You heard about today with the illegal alien coming in very sadly from Mexico," he said. "And you saw what happened to that incredible beautiful young woman," President Trump said.

"Should have never happened. Illegally in our country," Trump said. "We've had a huge impact, but the laws are so bad, the immigration laws are such a disgrace. We're getting it changed but we have to get more Republicans."

Immigration activists demand justice

that undocumented immigrants are more dangerous than US citizens. Trump has often suggested , erroneously,that undocumented immigrants are more dangerous than US citizens.

"The killer must be brought to justice. Let's also remember that this is a crime committed by an individual, NOT a community," immigration activist Erika Andiola tweeted. "Of course, there will be some trying to politicize this tragedy. At moments like this, we need leaders who bring us together and move us forward together, not those who exploit tragedy to further divide us. This murder DOES NOT represent me & my community. DON'T GO THERE."

Democrats and immigration advocates have said that by focusing on outlier criminal cases, Republicans and Trump are distorting the fact that immigrants are no more prone to criminal acts than the native-born population -- and some studies have found they are actually less likely to commit crimes.

Ali Noorani, the executive director of the National Immigration Forum, described it as an "awful tragedy," but warned that the suspect does not represent the values of the immigrant communities.

"The murderer should be brought to justice. He does not belong in the US, nor does he represent the hard work, compassion and contributions of the immigrants, documented or not, who live in the US."

As Iowans, we are heartbroken, and we are angry. We are angry that a broken immigration system allowed a predator like this to live in our community, and we will do all we can bring justice to Mollie's killer. — Gov. Kim Reynolds (@IAGovernor) August 21, 2018

US Sen. Chuck Grassley of Iowa said on the Senate floor Wednesday that Tibbetts' murder was "preventable." Improved technology and increased security personnel "could've prevented this man from crossing the border," he said.

Iowa Gov. Kim Reynolds said residents "are heartbroken, and we are angry" about what happened to Tibbetts.

"We are angry that a broken immigration system allowed a predator like this to live in our community, and we will do all we can bring justice to Mollie's killer," Reynolds said in statement.

We commend the swift action by local, state, & federal investigators working in Iowa in apprehending an illegal immigrant, who's now charged with first-degree murder. Now, justice will be served. We will never forget Mollie Tibbetts. — Vice President Mike Pence (@VP) August 21, 2018

Vice President Mike Pence, who met with Tibbetts's family last week during a visit to Des Moines, said he was "heartbroken" by the news.

"We commend the swift action by local, state, & federal investigators working in Iowa in apprehending an illegal immigrant, who's now charged with first-degree murder. Now, justice will be served. We will never forget Mollie Tibbetts," Pence said.