ALBANY — Attorney General Eric T. Schneiderman of New York asked Gov. Andrew M. Cuomo on Monday to immediately grant his office the power to investigate and prosecute killings of unarmed civilians by law enforcement officials.

Mr. Schneiderman also challenged state legislators to pass new laws to repair public confidence in the criminal justice system, which he said was badly damaged after grand juries in Missouri and on Staten Island declined to bring criminal charges against officers in fatal encounters with unarmed black men.

But he seemed unwilling to wait for new powers to investigate the police in the event that another killing occurred before new laws were passed. “When the trust between the police and the communities they serve and protect breaks down, everyone is at risk,” he said.

The grand jury’s decision not to indict in the case of Eric Garner, who died after a police chokehold during an arrest on Staten Island in July, has renewed and strengthened calls for special prosecutors to handle such cases.