MUMBAI, India — The video, widely circulated on social media this week in India, shows a man on the ground, pleading for his life before a mob kicks and beats him to death. He was one of seven men killed in two vigilante mob attacks in central India last week, at times as police officers looked on.

The two attacks last Thursday, within an hour’s drive of each other in the state of Jharkhand, underscored the lawlessness that continues to plague India even as it seeks to modernize its economy and society.

The attacks were incited by rumors on the messaging service WhatsApp warning of strangers who were abducting children. The stories proved entirely false.

The crowds swelled to more than 500 over several hours, and the men who were killed were innocent passers-by, the police said. “Not a single case of child abduction has been reported in this area,” said Shrikant Khotre, the assistant superintendent of police in Ghatsila, where one of the victims lived.

“The mobs have intentionally killed these men,” said Animesh Naithany, the deputy superintendent of police in Jharkhand. “They knew they were taking the law into their hands, and instead of turning them in to the police they killed them.”

Mr. Naithany said the police were still investigating who was behind the WhatsApp messages.

Episodes of mob violence occur with numbing regularity in India, typically without a great deal of scrutiny except when they are religiously motivated or involve attacks on women.

In March, a mob outside New Delhi attacked two Nigerian students after an unsubstantiated report that Africans had sold drugs to an Indian student who later died of an overdose.

In April, a 55-year-old Muslim man was killed in the state of Rajasthan after he was attacked by a crowd of about 200 Hindu vigilantes who believed he was transporting cows to slaughter. (Cows are sacred in Hinduism.)

This month, one person was killed and 16 injured in Uttar Pradesh when the Dalit community clashed with another group.

Analysts and officials say the vigilante violence stems from a variety of problems with the police and the judiciary. India has a low number of police officers per capita, and those on the job are often poorly trained, unprofessional and corrupt. Morale is low thanks to meager pay, long hours and little or no vacation time.

The judicial system is in perpetual crisis, with more than 40 percent of high court judgeships unfilled. This has produced an enormous backlog of cases, leading to long delays during which witnesses may die, flee or simply disappear.

Moreover, policing in most states is governed by colonial-era laws that allow politicians to control the transfer and appointments of top officials. In practice, this means they are heavily politicized, influenced by governing-party politicians rather than evenhandedly enforcing the law.

“All political parties don’t think beyond their own importance and power, so they don’t reform the police,” said Julio Ribeiro, a former police commissioner of Mumbai. “It’s only when the people demand real reform that we will have it, and they haven’t done that yet.”

The problems have convinced many Indians, particularly the indigent and illiterate, that if they are to have any justice at all, they must take the law into their own hands.

In an interview, Uttam Verma, a survivor of one of the mob attacks last week, recounted the terrifying series of events. Mr. Verma, 31, said he and his younger brother, Vikas, had ridden a motorcycle into the village of Nagadih, on the outskirts of Jamshedpur, the steel-producing city where they live. They were looking for land to start a new business making septic tanks.

“A little into the village, the road was obstructed by a pipe, and the villagers were sitting around armed with bows and arrows, axes and swords,” Mr. Verma said.

Mr. Verma said that he urged Vikas to turn back but that his brother insisted they continue looking for the land.

A group of villagers stopped them and accused them of being child thieves, Mr. Verma said. They demanded to see the brothers’ identification, which he had, but his brother did not.

The brothers called home, and another brother, Gautam, and a friend, Gangesh Gupta, rushed to the scene, along with the Vermas’ grandmother.

Before long, the crowd began attacking the group with bricks, sticks and swords, Mr. Verma said.

“We just could not comprehend what was happening,” he said. The crowd spoke a tribal language that he and his brother did not understand well.

“People started coming out of their homes, and the mob kept getting bigger,” he said. Police officers arrived at the scene but did not help them, he said.

“The policemen said: ‘Are they child stealers? Let’s put them in the vehicle and take them,’ ” Mr. Verma said.

Mr. Verma escaped, but the others could not.

“The next I saw of my brothers was as dead bodies,” he said, weeping.

His grandmother was in the hospital recovering from her injuries.

Radhey Shyam Gupta, 38, the uncle of Mr. Verma’s friend Gangesh Gupta, who was killed in the attack, said he was shocked when he saw his nephew’s body.

“His skull had cracked open and there was not a single part of his body which had not been hit and did not have marks,” Mr. Gupta said.

“The police were a silent spectator,” he added.

Prashant Anand, the superintendent of police in Jamshedpur, who is leading the investigation, said the mob far outnumbered the police.

He said the police had arrested five people and identified 17 as suspects. The head of the village is a suspect, but he has not yet been arrested, Mr. Anand said.

There were more than 500 people in the crowd trying to kill the three victims, Mr. Anand said, and only four police officers with the station head at the scene.

The same day, about an hour’s drive away, four cattle traders were also attacked by a mob, the police said. At least one of the men, Mohammad Naeem, was in the area to attend a family event, said Mr. Khotre, the assistant superintendent of police in Ghatsila, where Mr. Naeem lived.

A video shows Mr. Naeem surrounded by a mob of stick-wielding men. At one moment, his white undershirt covered with blood, he sits on the ground with his hands folded, apparently begging for his life.

Mr. Naithany, the deputy police superintendent in Jharkhand, said the vigilante mobs had sprung seemingly from nowhere, prompted by the WhatsApp messages.

“Rumors of children being abducted spread on WhatsApp like wildfire,” he said. “Villagers started keeping vigil around their villages. Since they are an illiterate lot, they cannot differentiate between a real piece of news and a rumor.”

Mr. Naithany said 20 people from the mob had been arrested on murder and rioting charges. An investigative team will submit a report within a month. The officers in charge of the police stations near both attacks have been suspended.