Activist groups in New York City have rejected a call by Mayor Bill de Blasio to hold off on any new demonstrations until after the funerals of two NYPD officers who were ambushed and murdered Saturday in Brooklyn.

The killings have aggravated tensions between police, City Hall, and protesters who have staged regular demonstrations since a Staten Island grand jury refused to indict an officer earlier this month in connection with the death of 43-year-old Eric Garner. Amateur video appeared to show the officer putting Garner in a chokehold while questioning him over the sale of untaxed cigarettes.

"We are in a very difficult moment. Our focus has to be on these families," de Blasio said Monday at police headquarters. "I think it's a time for everyone to put aside political debates, put aside protests, put aside all of the things that we will talk about in all due time."

However, the Rev. Al Sharpton told Reuters late Monday that de Blasio's request was too "ill-defined" to heed.

"Is a vigil a protest? Is a rally?" Sharpton asked.

Another group, The Answer Coalition, said it would go ahead with a long-planned march Tuesday evening, and denounced the mayor for what it called an "outrageous" attempt to chill free speech. The New York Post reported that a few dozen protesters staged a "die-in" at Grand Central Terminal before marching toward Times Square.

"We will not let recent tragic moments derail this movement," one protester shouted. "This is the revolution and we will not be repressed."

De Blasio's relations with the city's police unions have tumbled to an extraordinary new low following Saturday's shooting, which the gunman claimed was retaliation for the deaths of Garner and Michael Brown in Ferguson, Missouri.

In a display of defiance, dozens of police officers turned their backs to de Blasio at the hospital where the officers died Saturday night, and Patrolman's Benevolent Association President Patrick Lynch said the mayor had "blood on his hands" for enabling the protesters.

Late Monday, de Blasio and New York Police Commissioner William Bratton held a joint press conference at which Bratton claimed to have spoken with leadership of all the police unions, and claimed they have agreed on "standing down" until after the funerals of the officers.

The funeral for one of the officers, Rafael Ramos, is scheduled for Saturday. Arrangements for the funeral of his partner, Wenjian Liu, are pending the arrival of relatives from China.

Despite Bratton's apparent efforts at conciliation, the murders of Ramos and Liu has blown open a rift with the police force unlikely to heal soon. some pundits say the level of animosity between the unions and de Blasio had reached a critical point and the officers were even more inflamed than when thousands of officers stormed City Hall and stopped traffic on the Brooklyn Bridge in 1992 to protest Mayor David Dinkins' efforts to create a civilian oversight board.

Former New York Mayor Rudolph Giuliani accused de Blasio late Monday of fueling an "atmosphere of hate" toward officers.

"I don't put the blood of these police officers on the mayor's doorstep," Giuliani told Fox News. "I lost police officers, Bloomberg lost police officers. What I do hold him responsible for is letting those demonstrations get out of control. ... He's guilty of creating an atmosphere of police hatred in certain communities."

The Associated Press contributed to this report.