US President Donald Trump noted the arrest and called for immigration law changes at a rally in West Virginia.
Iowa's two Republican US senators described Tibbetts' death as a tragedy "that could have been prevented," and Iowa Governor Kim Reynolds said residents were heartbroken and 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 to bring justice to Mollie's killer," Reynolds, a Republican, said.
The arrest is likely to spark calls for a further crackdown on illegal immigration, which Trump has made 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 US residents are less likely to commit crime, several studies from social scientists and the libertarian think-tank Cato Institute find that is wrong and states with a higher share of people living in the country illegally have lower violent crime rates.
Trump asked his audience at a rally in Charleston, West Virginia, whether they had heard about the "illegal alien" from Mexico.
Trump said: "You saw what happened to that incredible, beautiful young woman. Should have never happened."
Trump called the nation's immigration laws "a disgrace" that need to be overhauled. He added, "We're getting them changed, but we have to get more Republicans. We have to get 'em."
US Immigration and Customs Enforcement said that it lodged a federal immigration detainer for Rivera after he was arrested on the murder charge. That move means the agency has probable cause to believe he is subject to deportation.
Investigators said they believed Rivera had lived in the area from four to seven years. Rahn declined comment on his employment history, but described Rivera as someone who lived in a rural area and kept to himself. 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 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.
An affidavit attached to the criminal complaint against Rivera alleged that he admitted to investigators he got out of his car and started running alongside Tibbetts.
Tibbetts grabbed her phone and said she was going to call the police. The affidavit says Rivera panicked and then said he blacked out. Rivera next remembers seeing her earphones on his lap, and taking her bloody body out of the trunk of his car, it said.
"The defendant further described during the interview that he dragged Tibbetts on foot from his vehicle to a secluded location in a cornfield," the affidavit said.
Investigators said they had earlier searched the area for Tibbetts but didn't find her, noting the body was covered by corn stalks when recovered.
Rahn said that Rivera was cooperating with investigators and speaking with the help of a translator. He said an autopsy would be performed on the body tomorrow by the state medical examiner's office, which would assist investigators in understanding whether Tibbetts had been assaulted or tried to fight him off.
Rivera's initial court appearance is scheduled for tomorrow in Montezuma.
A conviction on first-degree murder carries a mandatory sentence of life in prison without parole in Iowa, which doesn't have the death penalty.
- AP
