By Lizette Alvare

MIAMI, 2/24/15 — The Justice Department on Tuesday closed its investigation into the shooting death three years ago of Trayvon Martin, the unarmed black teenager in a hoodie who became a symbol of racial profiling and the face of a protest movement, without filing hate-crime charges against the gunman, George Zimmerman.

The department began its civil rights investigation shortly after a national furor erupted over Mr. Martin’s death in Sanford, Fla., which set off protests, demands for justice and an emotional response from President Obama. The shooting was the first in a string of racially tinged cases involving the deaths of young black men that have prompted a rethinking of the nation’s criminal justice system.

Mr. Zimmerman was acquitted of second-degree murder in a state court in 2013; some jurors said they believed that he had shot Mr. Martin, 17, in self-defense.

The conclusion of the investigation came as Attorney General Eric H. Holder Jr. neared the end of his tenure. The shooting was one of several racially fraught cases that Mr. Holder said the department would finish investigating before he stepped down.

The Justice Department is also conducting two civil rights investigations into the shooting death of Michael Brown, another unarmed black teenager, who was killed by a white police officer in Ferguson, Mo., in August. In that case, violent protests erupted after the shooting. A grand jury declined to indict the officer.

Other police-involved deaths, including the choking of an unarmed man in Staten Island and the shooting of a Cleveland boy holding a realistic, airsoft-style gun, have fueled concerns about police conduct and racial profiling.

The lawyer for Mr. Martin’s family, Benjamin L. Crump, said the parents, Sybrina Fulton and Tracy Martin, were badly shaken by the news that the federal government would not bring charges. The family met with Justice Department officials in Miami on Tuesday. “This is very painful for them; they are heartbroken,” Mr. Crump said. “But they have renewed energy to say that we are going to fight harder to make sure that this doesn’t happen to anybody else’s child.”

Ms. Fulton and Mr. Martin have become national figures and, through their foundation, are trying to help reduce violence in black and Hispanic communities and expand educational opportunities for minority students.

Since his acquittal, Mr. Zimmerman has had numerous run-ins with the law. Last month, he was arrested and charged with aggravated assault, accused of throwing a wine bottle at his girlfriend. In 2013, shortly after his acquittal, he was arrested after a heated fight with another girlfriend, but the woman asked prosecutors not to press charges. And in 2014, the police in Lake Mary, Fla., said a driver had told officers that Mr. Zimmerman threatened him during what was described as a road rage incident.

The federal inquiry was started to pursue “an independent investigation” into the shooting after local police officials and prosecutors were slow to arrest and charge Mr. Zimmerman; they argued that Florida’s self-defense laws would make it difficult to prove a criminal case. Gov. Rick Scott then appointed a special prosecutor who eventually charged Mr. Zimmerman.

Federal investigators interviewed 75 witnesses, reviewed all the material gathered by the State of Florida and examined evidence relating to Mr. Zimmerman’s encounters with law enforcement after his acquittal, according to a statement. But none of that was enough to prove that Mr. Zimmerman, who is part Peruvian, killed Mr. Martin because of his race.

The bar for prosecuting hate crimes is high — proving negligence or recklessness is not enough — and Mr. Holder said the “standard for a federal hate crime prosecution cannot be met under the circumstances here.” Mr. Zimmerman’s former lawyer, Mark O’Mara, has said his client is not a racist, saying he has black friends and mentored two black youths.

The Justice Department’s investigation into the Ferguson case is no less difficult, and is perhaps even tougher, because it focuses on a police officer who fired his weapon in the line of duty.

Mr. Zimmerman’s case also swirled, to a large extent, around issues of race. Prosecutors said Mr. Zimmerman forced a confrontation with Mr. Martin on Feb. 26, 2012, because Mr. Martin was an unfamiliar tall black teenager in a hoodie walking around Mr. Zimmerman’s gated community one rainy night. Mr. Martin was in Sanford with his father, visiting his father’s fiancée.

A rash of burglaries in the area had heightened Mr. Zimmerman’s concerns, and as the neighborhood watch leader, he said, he was suspicious of Mr. Martin. He got out of his car — ignoring the advice of a police dispatcher — and followed Mr. Martin, setting off a confrontation that led to Mr. Martin’s death, prosecutors said.

Angry at Mr. Zimmerman and feeling threatened, Mr. Martin pushed him to the ground, punched him and slammed his head into the pavement, leaving visible wounds, defense lawyers said. Mr. Zimmerman, flat on his back, took out a gun and killed Mr. Martin. He told the police it was self-defense.

Matt Apuzzo contributed reporting from Washington.