Chicago's top prosecutor on Thursday said she asked the U.S. Federal Bureau of Investigation to help probe the fatal police shootings of two black residents over the weekend, as protesters renewed calls for the resignation of Mayor Rahm Emanuel.

The unusual step ramps up pressure on the Chicago Police Department, which is already the subject of a U.S. Department of Justice civil rights investigation over its use of deadly force, especially against minorities.

Cook County State's Attorney Anita Alvarez said on Thursday she wants help investigating the shootings of Bettie Jones, a 55-year-old mother of five, and Quintonio LeGrier, a 19-year old college student, by a single Chicago police officer.

Police, who were responding to a call that LeGrier was threatening his father with a baseball bat, have admitted that Jones' shooting was accidental.

"This is a deeply disturbing incident that demands a very deliberate and meticulous independent investigation," said Alvarez.

Shootings of blacks by mainly white police officers in several cities over the past 18 months have led to protests across the country. Cleveland is expecting to see its fourth day of demonstrations following a decision on Monday not to charge officers who shot and killed a 12-year-old boy playing with a toy gun.

In Chicago, protesters at City Hall on Thursday punched a papier mache effigy of the mayor's face and chanted "Hey, hey! Ho, ho! Rahm Emanuel has got to go." They also planned a protest in front of Emanuel's house.

Protests against both Emanuel and Alvarez have been staged almost daily since late last month when the nation's third-largest city released video showing a white Chicago police officer, Jason Van Dyke, shooting a black teenager 16 times in October 2014.

Van Dyke was charged on Nov. 24 with Laquan McDonald's murder and this week pleaded not guilty. Critics say it took too long to both charge Van Dyke and release the video.

The weekend shootings of Jones and LeGrier increased tensions in Chicago, forcing Emanuel to return early from a family vacation to deal with the fallout.

Emanuel on Wednesday announced that Chicago police will get new equipment - including generally non-lethal Tasers - and training to help them defuse tense situations and limit use of lethal force.

Hundreds of protesters also gathered on Thursday on Chicago's most prestigious shopping district, called the Magnificent Mile, to protest all gun violence. Chicago has seen 2,360 shootings in 2015, up 17 percent over 2014.

Among the marchers was Lutrice Boyd, whose son Frederick James Giles III, 21, was killed in 2012. "I haven't been whole since my child has left," said Boyd.

(Reporting by Mary Wisniewski and Justin Madden in Chicago; Additional reporting by Kim Palmer in Cleveland; Editing by Bill Rigby)