The shooting deaths of two New York City police officers Saturday are drawing new attention to the role that social media networks play as a platform for threats of violence, particularly against police and other law enforcement officials.

Ismaaiyl Brinsley, the officers’ alleged killer, posted a number of anti-police and anti-government messages online in the weeks before the killings, including one on Instagram just hours before the officers were shot and a photo of a pistol and bloodstained pants with the caption: “I’m putting Wings on Pigs Today.”

“That seems to be the rage here, anti-government and anti-police,” Robert K. Boyce, the NYPD’s chief of detectives, said Monday.

Police departments across the country are moving quickly to harness the reach and transparency of these networks as tools to investigate and, they hope, neutralize the potential for violence.

“If you see something on social media that is a threat against a police officer, call 911 immediately,” New York Mayor Bill de Blasio (D) implored the city’s residents. “We would much rather get too much information than too little. . . . Once this individual posted on Facebook his intention, anyone who sees that has the obligation to call the police immediately and report it. We cannot take this lightly.’ ”

Increasingly, departments are using social media such as Facebook and Twitter as intelligence-gathering tools and vehicles for community outreach.

Kenneth S. Springer, a former FBI agent who runs Corporate Resolutions, a New York-based firm that spots online threats and risks for corporate clients, said the Internet is the equivalent of a wiretap for the 21st century.

“Back in my day, the FBI had wiretaps or surveillance to find out where people will be meeting. Now it’s monitoring the Internet,” he said. “That’s why law enforcement is going to have to devote more resources to this. And hopefully they’ll thwart the next thing such as this.”

Tim Burrows, a retired Toronto police sergeant who advises police departments on social media strategy, said: “A lot of the monitoring and listening tools police were using up until very recently has been very focused on overt activity.”

But Burrows said that Saturday’s killings are likely to cause departments to monitor social media threats more closely, even though most of that kind of talk may just be idle chatter. “Police would rather chase down 1,000 false leads than see something that happened in Brooklyn Saturday,” he said.

In Newark, Police Director Eugene Venable said that in light of Saturday’s shootings, Newark officers will no longer patrol alone and that the department has stepped up its monitoring of online threats against police.

“They’ve been on high alert ever since the killings happened Saturday,” Venable said. “Every day, they’re checking more than they would be normally. They’re looking for threats all across this state and nation.”

Venable said that the department has also asked officers to refrain from expressing opinions online about the Michael Brown and Eric Garner cases as a way to “try to get the hostility down” and foster better relations between police and communities. Venable said the Newark department typically looks to social media posts for potential evidence in cases.

In Houston, Police Chief Charles A. McClelland Jr. urged his officers to be more vigilant, and the department reported that a number of Web users had visited its Facebook page after the New York killings to report an online threat made against police officers. Houston police spokesman John Cannon said there was “no specific threat discerned” from the posting.

Distinguishing dangerous threats from constitutionally protected, if vitriolic, free speech can often be difficult for police. Credible threats that would warrant police action “have to be unequivocal,” said Danielle Citron, a professor at the University of Maryland School of Law. “They have to target specific people, and they have to state a present threat [of] violence.”

Speech that is angry or merely inflammatory is probably protected by the First Amendment, Citron said. The issue has made its way to the Supreme Court, which is reviewing a case in which the central question is whether a man’s messages of violence to his ex-wife on Facebook constituted a “true threat.”

In Seattle in 2009, a man who had expressed anti-police sentiments was accused of firebombing police cars and eventually fatally shooting an officer and wounding another. Since then, said Detective Drew Fowler, a spokesman for the Seattle Police Department, threats against the police are “on our minds always.”

The Seattle department has won praise for its social media presence, which includes a Twitter account with more than 91,000 followers. Fowler said that if officers have concerns about online posts, they forward them to detectives but that it is sometimes difficult to distinguish intent online.

“People say pretty inflammatory things online, shielded by a computer screen,” he said. Sometimes discerning “what is a threat and what is a rant is not the simplest thing.”

Sometimes, 21st-century technology can run into antiquated police procedures and other obstacles to information sharing between departments.

On Saturday, Brinsley allegedly shot his former girlfriend outside Baltimore. The woman’s mother told Baltimore County police that Brinsley was posting on the woman’s Instagram account through her cellphone. Baltimore County police tracked the cellphone to Brooklyn. They called a local precinct, faxed a “wanted” poster to New York police and called the city’s real-time crime center. By the time that process was finished, Brinsley had killed the two officers.

“Even in the way the alerting system works, maybe law enforcement has to look at that as well,” Burrows said. “There are the agencies that still think the fax machine is the best way to communicate, and we’re slowly trying to draw them into the 21st century.”

In Minneapolis, police spokesman John Elder said the department is keeping an “extra eye” online for threats. The department uses social media in different ways in different divisions — detectives use it as an aide in crime-solving, and the media relations arm of the force uses it to interact with the community.

In Boston, the police department won plaudits for its use of Twitter for keeping the public informed after the Boston Marathon bombings and during the search for the two suspects.

And police departments have used social media platforms including Pinterest to disseminate mug shots and photos of missing persons. Fowler said Seattle police have found that having a robust social media presence can help solve crimes.

“When the time comes and there’s a child missing, we put it out on Twitter, and we find them in 10 minutes,” he said.