New York state's attorney general has asked the governor to authorize his office to investigate deaths at the hands of police following the public outcry over the killing of an unarmed Staten Island man.

Attorney General Eric Schneiderman, in a letter Monday to Gov. Andrew Cuomo, said that authority exists under New York law, has been used in the past and is needed now because of the "crisis of confidence" in law enforcement.

The attorney general's authority would apply to cases after the executive order is signed and last until the state Legislature acts to permanently address the issue.

It wouldn't apply to the case of Eric Garner, who died after a confrontation in July with several New York City police, including an officer who used an apparent chokehold. Video of the incident was recorded by a bystander and posted on the Internet.

Federal authorities are now investigating that case after Staten Island District Attorney Dan Donovan investigated and a grand jury declined to indict any officers. In suburban St. Louis, a grand jury declined to indict an officer who shot an unarmed 18-year-old man to death.

"In New York, and across the country, the promise of equal justice under law has been eroded by a series of tragedies involving the death of unarmed persons as a result of the use of force by law enforcement officers," Mr. Schneiderman wrote, noting the victims are often minorities. "All too often, the families of the victims and the members of their communities are left with the belief that our criminal justice system has both unjustly targeted and inexplicably failed them."

The Cuomo administration is reviewing the proposal in a broader review with stakeholders and criminal justice experts, a spokeswoman said. "When people begin to lose faith in the criminal justice system, reform must follow," she said.

More than two dozen city and state officials offered public support for the proposal Monday.

"It is imperative that a separate prosecutor—with no connection to the local police department—pursue police misconduct cases," said the city's public advocate, Letitia James, who has long called for independent prosecutions. "We need to remove the conflict of interest. We need to remove the appearance of bias."

Mr. Donovan's office declined to comment.

Brooklyn District Attorney Ken Thompson said he's adamantly against Mr. Schneiderman's proposal. "Local prosecutors who are elected to enforce the laws in those communities should not be robbed of their ability to faithfully and fairly do so in cases where police officers shoot, kill or injure someone unjustly," he said.

Bronx District Attorney Robert Johnson said his office has prosecuted several police officers and the issue should be studied carefully with district attorneys' input. Those cases included four city police indicted for murder for shooting unarmed Amadou Diallo 19 times in the vestibule of his apartment building in 1999. An Albany jury later acquitted them.

The attorney general, whose office needs referrals from the governor or other agencies to prosecute cases, said many people believe the close working relationships between police and local prosecutors influences how vigorously cases are pursued. Mr. Schneiderman said he believes "the overwhelming majority" are capable and have an ethical duty to see justice is done.

"The question is whether there is public confidence that justice has been served, especially in cases where homicide or other serious charges against the accused officer are not pursued or are dismissed prior to a trial by jury," he wrote.

He told reporters Monday that the most troubling words came from Mr. Garner's widow after the grand jury decision: "Oh my God. Are you serious?"

Mr. Schneiderman noted that legislation has been introduced to authorize his office to investigate and prosecute any crime allegedly committed by police or in cases where a judge finds a county prosecutor disqualified.

He requested an immediate order from Mr. Cuomo to investigate and present grand jury evidence in any death of an unarmed person by police. "I would further respectfully request that, to avoid the possibility of compromising any local, state or federal investigations already in progress, the order apply only to incidents occurring on or after the date the order is signed."