Georgia lawmakers voted on Thursday to tighten the state’s already strict immigration laws in response to the killing of Laken Riley, a 22-year-old nursing student, whose death became ensnared in the broader fight over immigration policy after a man from Venezuela who entered the country illegally was charged with her murder.

In the frenzied final hours of the legislative session, the state’s House of Representatives gave final approval to a measure that would require local law enforcement agencies to scrutinize the immigration status of people in their custody and to cooperate with federal immigration authorities.

The legislation was the result of a vow from Republican lawmakers to crack down after Ms. Riley’s body was found last month in a wooded area on the University of Georgia campus in Athens. Her death rattled the community that is the home of the state’s flagship university, roughly 70 miles from Atlanta.

The case quickly reverberated beyond Georgia, with Republicans arguing that her killing exemplified a failure by President Biden to adequately respond to an influx of migrants.

Gov. Brian Kemp of Georgia, a Republican, denounced “an unwillingness by this White House to secure the southern border.” Ms. Riley’s death was also invoked during the State of the Union as President Biden responded to heckling from the Georgia representative Marjorie Taylor Greene.

“An innocent young woman who was killed by an illegal,” Mr. Biden said, veering from his script — a statement that prompted a backlash from liberal Democrats and immigration advocates, particularly over his use of the term “illegal,” which they condemned as a dehumanizing pejorative.

Proponents of tougher immigration laws have zeroed in on the case because the man charged in the killing, Jose Antonio Ibarra, was arrested by the Border Patrol for entering the United States illegally in 2022.

He was released with temporary permission to stay in the country through parole, a practice that the Biden administration halted last year. Officials said that Mr. Ibarra had been arrested by the police in New York for driving a scooter without a license and with a child who was not wearing a helmet. He was arrested again, this time in Georgia in October, in connection with a shoplifting case and was released.

Lawyers representing Mr. Ibarra in the murder case have requested a jury trial. He remains held without bail.

Federal legislation named for Ms. Riley passed in the U.S. House of Representatives this month, with 37 Democrats joining Republicans in support of the measure that would mandate that migrants who enter the country without authorization and are accused of theft be taken into federal custody. The bill has little chance of advancing in the Senate, and critics have assailed the legislation as a craven exploitation of a tragedy.

In Georgia, the bill being sent to the governor would require local law enforcement officials to seek to verify the immigration status of any person in their custody who lacks documentation and to notify federal immigration officials when they detain someone who is not a legal resident. Local law enforcement agencies would also be required to routinely release data documenting the number of cases reported to federal authorities and the responses.

“I think this truly is a common-sense measure,” said State Representative Houston Gaines, a Republican whose district includes Athens. “What we’re talking about is individuals who are in the country illegally that have committed offenses, additional criminal offenses, and making sure that those individuals are held accountable.”

The bill formalizes what has long been the standard practice of many law enforcement agencies in the state and adds penalties for failing to comply, like the loss of state and federal funds.

“It is an expansion of the existing law,” said J. Terry Norris, the executive director of the Georgia Sheriffs’ Association. “It has more teeth.”

The legislation has been criticized for having vague language and placing an unfair burden on local officials, who could face lawsuits. The bill has also spurred fears of increased racial and ethnic profiling by the police.

Supporters of the measure contend that law enforcement officials have not been notifying federal authorities and that a more stringent requirement was necessary. “Every sheriff must by law report when an alien is in his jail,” said State Representative Jesse Petrea, the Republican sponsor of the bill. “Our concern is that not everybody has been doing that.”

But Mr. Norris challenged that. He said that a statewide survey showed that the 142 sheriffs who operate jails all said they were already reporting that information to Immigration and Customs Enforcement.

By the conclusion of the session after midnight, lawmakers had failed to advance another measure prompted by Ms. Riley’s death, this one essentially deputizing members of the public to sue local governments over policies that provide sanctuary to undocumented immigrants.

That measure, which overtook a bill originally regarding penalties for passing stopped school buses, was meant to bolster longstanding state laws that forbid Georgia municipalities from becoming “sanctuary cities” providing safe harbor to immigrants who entered the United States illegally. Local government could lose state and federal funds if a judge were to find that the policies indeed violated state law.

Critics have attacked the legislation as an overreaction that took advantage of the anguish unleashed by Ms. Riley’s death. The legislation also interferes with the authority of local governments — denying them of the ability to define “their own approaches to immigration that work for each community,” said State Senator Josh McLaurin, a Democrat.

“I think reasonable people can disagree about how to do immigration policy,” he said. “But where the majority has really overreached with these bills is by making the penalties and requirements so severe that they’ve essentially denied the ability of a local government to be its own independent government.”