NEW YORK (CBSNewYork/AP) — The family of Eric Garner will rally outside City Hall Tuesday calling for justice on the fourth anniversary of his death.

For his family, it’s been four years of limbo, CBS2’s Janelle Burrell reported.

“I still have sleepless nights,” his mother, Gwen Carr, said Monday. “I still have nightmares.”

Garner died while being arrested for selling loose cigarettes. Cell phone video showed Officer Daniel Pantaleo putting Garner in an apparent chokehold.

Garner, who had asthma, is heard gasping, “I can’t breathe.” He was pronounced dead at a hospital. The medical examiner ruled the death a homicide caused in part by the chokehold.

A grand jury declined to indict Pantaleo and the Justice Department launched a civil rights investigation.

Typically, the police department waits for federal prosecutors to conclude civil rights violations inquiries before taking action.

But in a notice to the Department of Justice on Monday, the NYPD told DOJ officials that they’re moving forward by the end of next month whether the federal case has concluded or not.

“Based on our most recent conversations, it has become clear that a definite date by which time a final decision by the U.S. DOJ will be rendered in this matter cannot be predicted,” Lawrence Byrne, deputy commissioner for legal matters, wrote to prosecutor Paige Fitzgerald.

“The NYPD has come to the conclusion that given the extraordinary passage of time since the incident without a final decision on the U.S. DOJ’s criminal investigation, any further delay in moving ahead with our own disciplinary proceedings can no longer be justified,” Byrne added.

A police watchdog agency, the Civilian Complaint Review Board, will prosecute Pantaleo under a memorandum of understanding with the NYPD, according to Byrne.

Mayor Bill de Blasio praised the police department’s decision.

“I think NYPD is right to proceed and they’re giving the Justice Department one final chance,” he told NY1.

But Garner’s family and supporters are accusing the mayor of inaction and misleading the public. They’re calling for Pantaleo’s disciplinary proceedings to begin immediately.

“We want to see this done,” Carr said. “We just want justice for my son, Eric. It’s not just for Pantaleo. It’s for the other five officers who was involved.”

“Please move forward on this and fire those officers,” she added. “All of them.”

In a statement, the DOJ said it already told the police department in the spring it could go forward and that the move “does not have any bearing on the decision-making timeline.”

A lawyer for Pantaleo, who’s been on paid desk duty, declined comment on Monday.

Pat Lynch, head of the Patrolmen’s Benevolent Association, called on the DOJ to close its case but said that the officer deserves due process in the disciplinary process.

Garner’s family received $5.9 million from the city in 2015 to settle a wrongful death claim.

(© Copyright 2018 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)