Jorge Rios, 33, was arrested on March 31, a week after the body of Caroline Cano, 45, was found floating in a lake in Lincoln Park, Jersey City.
Rios sexually assaulted Cano before strangling her as she struggled underwater, according to prosecutors.
Rios, whose full name was identified by immigration officials as Jorge Alberto Rios-Doblado, is a native of Honduras, according to Immigration and Customs Enforcement (ICE).
An ICE spokesman that the agency placed a detainer on Rios following his arrest, meaning if he is released either without being convicted or after serving time, he will be deported again.
"ICE maintains that cooperation by local law enforcement is an indispensable component of promoting public safety. ICE will seek taking custody of Rios at the conclusion of his criminal proceedings, despite limited cooperation in the state," the spokesman said.
Rios faces up to 30 years in prison if convicted.
Hudson County Prosecutor Esther Suarez wrongly stated that Rios did not have a criminal record. Entering the United States illegally is a crime. She also told community members on April 2 to stop reading news websites and newspapers and instead listen to authorities in the city.
“I think you need to do some sort of social media, and I would tell you if you can, go to the Twitter feed for the County and the Prosecutor’s Office for Jersey City. I think that’s where you are going to get really your best information,” she continued.
As Suarez spoke, Jersey City Mayor Steven Fulop was seen smiling before looking at his cellphone.

Fulop said that a 2007 directive from the state's attorney general requiring all law enforcement officers who make arrests for indictable crimes to inquire about the alleged criminal's citizenship, nationality, and immigration status would not be followed by officers in Jersey City.
The order was unanimously supported by the Jersey City, City Council. Council President Rolando Lavarro claimed that the action would "send a resounding message" to President Donald Trump, who has attempted to crack down on the influx of illegal aliens into the United States.
After Rios allegedly raped and murdered Cano, people criticized the policy.

Jersey City Councilman Rich Boggiano, who supported the sanctuary city order, said that the Lincoln Park killing highlights why the United States needs to "close the border."
"How long are we going to tolerate people's children being murdered?" Boggiano said. "I have nothing against people coming to this country … If you’re a convicted criminal or deported you should not be able to get back in the country.”
Fulop's office declined to comment while the office of Lavarro did not respond to a request for comment.
