WASHINGTON -- New York City's police unions have agreed to refrain from putting out more statements on Saturday's cold-blooded murder of police officers Wenjian Liu and Rafael Ramos, after the unions came under scrutiny for blaming Mayor Bill de Blasio (D) for the shooting.

Ismaaiyl Brinsley, the man who killed the two officers, shot his former girlfriend in Maryland before heading up to New York and killing Liu and Ramos on Saturday. Before his rampage, Brinsley put a photo on Instagram, threatening to put "wings on pigs" and adding the hashtags used to support Michael Brown and Eric Garner, two unarmed African-American men whose deaths at the hands of police officers have sparked national protests in recent months.

De Blasio has repeatedly praised the work of law enforcement, but he has also called for reform to ensure that every New Yorker feels like he or she is getting fair treatment from the police. Pat Lynch, president of the city's largest police union, the Patrolmen's Benevolent Association, seemed upset that de Blasio has shown sympathy with the protesters.

"There's blood on many hands tonight," Lynch said Saturday night. "That blood on the hands starts at City Hall in the Office of the Mayor."

Another union, the Sergeants Benevolent Association, also went after de Blasio on Twitter Saturday:

The blood of 2 executed police officers is on the hands of Mayor de Blasio. May God bless their families and may they rest in peace. — SBA (@SBANYPD) December 21, 2014

During a press conference Monday afternoon, NYPD Commissioner Bill Bratton said the unions had agreed to stop putting out statements out of respect for Liu's and Ramos' families. De Blasio also called for a temporary halt to the protests to allow the families to mourn.

"I've had the opportunity today to talk with the leadership of all five of our police unions, in line with what the mayor has referenced, asking that demonstrations and other forms of protests be put on hold until after the Christmas holidays and after the funerals," said Bratton. "In discussion with the five presidents of our various unions, they are standing down in respect for the fallen members until after the funerals, and then we can continue the dialogue that had begun about issues and differences that exist."

De Blasio -- along with President Barack Obama and Attorney General Eric Holder -- have been taking a significant amount of heat from some conservatives for sympathizing with the grievances of protesters who are calling for fair treatment from law enforcement. On Monday, Rep. Pete King (R-N.Y.) accused Obama and de Blasio of creating an anti-cop environment that encouraged Brinsley.

But the unions swiftly came under a fair amount of criticism for their remarks as well.

"Much like we shouldn't be blaming a president for the deaths of soldiers on the battlefield, let's not point fingers at the mayor for a madman's actions. It's ridiculous to believe that if only de Blasio had been more like Rudy Giuliani, Officers Liu and Ramos would be alive," said NY1 Political Director Bob Hardt in a column. "It's the same sloppy and dangerous logic in which people tried to blame American foreign policy for the 9/11 attacks, saying the chickens have come home to roost. There are plenty of chickens that fly around on their own."

De Blasio also isn't the first mayor to get into an argument with the PBA; the union has gone after at least the last four New York City mayors.

Bratton made a similar point during Monday's press conference.

"Can you point out to me one mayor that has not been battling with the police unions in the last 50 years? Name one. Name one. So the experience of this mayor in terms of some cops not liking him -- it's nothing new," said Bratton. "It's part of life. It's part of politics. It is what it is. This is New York City; we voice our concerns and our opinions.

Bratton added that he is happy to resume the dialogue "once we get our officers respectfully mourned and buried."

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