(AP) -- Police departments across the country on Friday reacted to the deadly sniper attack on officers in Dallas with a mix of sorrow for the victims and concern for their own ranks, with many taking precautions to guard against copycats and other potential threats.

Outside New York Police Department headquarters, officers stood at attention as an American flag was lowered to half-staff to honor the five officers killed and seven wounded on Thursday in Dallas during a protest over fatal police shootings of black men.

Inside headquarters, Police Commissioner William Bratton met behind closed doors with Mayor Bill de Blasio and the NYPD's top commanders to discuss how to react to the killings. Pairs of NYPD officers were posted in front of the entrances to precinct stations across the city.

"It's a tragic time," Bratton told reporters when he emerged from the meeting. "It's just so hard to comprehend. What happened to these officers could have happened in any city in the country."

The Dallas officers were killed, he added, "just because they were wearing the blue uniform."

Patrick Lynch, head of the Patrolmen's Benevolent Association in New York, said in a statement that his membership was mourning the deaths and offering support to their families.

"They did nothing to harm anyone, but instead were protecting the rights of others to be heard in protest," Lynch said.

In New York, the slayings in Dallas were a tragic reminder of the 2012 ambush killing of two police officers by a gunman claiming retaliation for the police-involved deaths of Eric Garner in New York and Michael Brown in Ferguson, Missouri. The shooter killed himself.

After the Dallas killings, the most common safety measure for forces that normally allow officers to patrol alone -- including Chicago, Las Vegas, Cincinnati and Louisville, Kentucky -- was to order them to team up in pairs.

"It's a good time to double up in the interest of safety and to give officers the opportunity to talk to one another and decompress," said Dwight Mitchell, a spokesman for Louisville police.

The directive in Chicago came after officers working overnight there heard dispatchers broadcast a message urging them to "use extreme caution" after the Dallas attack. Elsewhere, officers were reminded to always wear their bulletproof vests.

Departments in New York City, Orlando, Florida, Buffalo, New York, and other cities were the target of vague, anonymous threats on social media and by telephone. The threats were being checked out, but there were no reports that any were viable.

The concerns come amid ongoing protests over the police killings of black men in Baton Rouge, Louisiana, and Falcon Heights, Minnesota, that have shown a potential to turn violent. During a demonstration Thursday night in Oakland, California, protesters blocked a highway, set a fire and broke windows of businesses.

A top police union leader in New York criticized the NYPD brass on Friday for not making sure officers were more heavily armed when assigned to the front lines of street protests.

The commanders are "trying to be politically correct at the expense of police officers who are trying to protect the public," said Ed Mullins, head of the Sergeants Benevolent Association.

While NYPD officials promised a heavy police presence at future protests, de Blasio indicated in a radio interview that there would still be an emphasis on restraint.

"Our officers want protests to be peaceful and they know that they're there, under the constitution, to protect the right to protest," he said.

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Associated Press writer Ezra Kaplan contributed to this report.