MEXICO CITY — Mothers rushed to pull their kids out of school, shopkeepers slammed down their metal gates, and bus drivers radioed one another about streets to avoid after false rumors of shootouts and gunmen traveling in a caravan in a Mexico City suburb began circulating on social networks.

The false reports of violence and impending attacks in Nezahualcoyotl soon included nearby suburbs and at least one borough in the capital, spreading panic and prompting police to take to the streets in force while officials turned to Twitter, television and even hand-distributed flyers to deny the rumors.

Twitter and Facebook are often used to warn of gunbattles and other dangers in Mexico’s violence-wracked cities, but the last two years have also seen social networks used to spread false warnings that have caused chaos in several cities. Mexico City has avoided large-scale violence, although drug-related killings and other crime have hit some of its suburbs, like Nezahualcoyotl.

In Nezahualcoyotl, to the west of the capital, authorities have received more than 3,000 phone calls with false reports of violence since Wednesday night, when the rumors began, city council spokesman Luis Percastre said Friday.

“They told us an indoor farmers market had been set on fire and we went to check — and nothing, it was working fine. Then someone else called to report a bank on fire and we also went — and nothing,” Percastre said.

Authorities deployed all police officers available throughout the crowded suburb and even called in two state police helicopters to patrol, he said. Prosecutors said five men had been arrested on charges of disturbing the peace Thursday night by running into a bakery in the neighboring Mexico City borough of Iztapalapa and shouting that members of criminal groups were coming to the area to cause problems.

One tweet read: “Warning: Cd. Neza has been taken by masked gunmen, cutting phone lines.” Another warned of gunfire: “Don’t get close to the train tracks, there is shootings, they are stealing everything.”

“These are people with dark objectives who tried to destabilize the city and were able to instill fear in people and make them take refuge at home for a few days because they started a psychosis,” Percastre said.

On Thursday, several schools suspended classes, some businesses remained closed and pedestrian and motor traffic declined notably in Nezahualcoyotl, a city of 1.1 million people, as rumors gained strength and began spreading to Iztapalapa.

Iztapalapa’s borough government said in a statement Friday that its emergency center had received more than 1,300 phone calls echoing the rumors.