ISLAMABAD, Pakistan — At first, the police described a weekend shooting in central Pakistan as a successful operation against a group of terrorists: four dead, including a middle-aged couple, their daughter and another man.
Then the couple’s children — a boy and two girls who survived the firefight with minor injuries — told a story about police brutality that was painfully familiar to Pakistanis, and the authorities arrested more than a dozen police officers, the prime minister demanded answers, and officials were left struggling to explain what happened.
From a hospital bed near his younger sisters on Saturday, Muhammad Umair, 9, told local journalists that his family had been traveling on Saturday from Lahore, the capital of Punjab Province, to a town in the region’s south to attend a wedding. They were stopped near the city of Sahiwal by police officers belonging to the counterterrorism department, he said.
“My father said to the police, ‘Take the money, but let us go,’” Muhammad Umair said.
But the police opened fire, killing his father, Muhammad Khalil, a 43-year-old grocery store owner; his mother, Nabila; his 12-year-old sister Areeba; and a family friend, 36-year-old Zeeshan Javed.
The authorities said Saturday that the family opened fire on police officers after they were asked to stop their car and an accompanying motorcycle near a traffic toll plaza. Two men on the motorbike managed to flee from the scene, according to the police.
Mr. Javed, the authorities said, was part of a group of militants affiliated with the Islamic State and was carrying weapons and using his friend’s family as a shield.
Contradicting that account, local news media, citing eyewitnesses, reported that the traveling family did not open fire on the police and that no weapons were recovered from their vehicle.
As news spread and cellphone footage of the aftermath went viral on social media networks, public outrage grew around the country.
Prime Minister Imran Khan expressed horror on Sunday.
“Still shocked at seeing the traumatized children who saw their parents shot before their eyes,” he said on Twitter. “Any parent would be shocked as they would think of their own children in such a traumatic situation.”
Mr. Khan, who had promised police reforms during his election campaign last year, vowed “swift action” after an investigation into the shooting. “Everyone must be accountable before the law,” he said.
Incidents of police abuse and extrajudicial killings are not uncommon in Pakistan, and the abusers often escape accountability. The police in Punjab, the most populous and prosperous of the country’s four provinces, are especially notorious for abuse and corruption.
A civil rights movement challenging law enforcement abuses gained momentum last year, after Rao Anwar, an influential police commander in the southern port city of Karachi was arrested over his role in a police shootout.
The police there claimed that the shooting had killed a Taliban militant. In reality, he was a 27-year-old shopkeeper and aspiring model named Naqeebullah Mehsud who was popular on social media, and had no links to militants.
The protests after the killing of Mr. Mehsud, an ethnic Pashtun, mushroomed into a movement in the country’s northwest, which has a majority Pashtun population. The Pashtun Tahafuz Movement, as the campaign is known, has challenged the authorities over abuses, and accused the Pakistani military, especially, of human rights violations, mass killings and extrajudicial abductions.
The Pakistani military has denied the allegations and in recent months has imposed limits on the news coverage of the movement.
Commander Rao is facing a Supreme Court-led inquiry, and is free on bail. Despite the arrest, few believe the police in this case or others will be made accountable.
Sardar Usman Buzdar, the chief minister of Punjab Province, promised justice when he visited the surviving children of the shooting Saturday at the hospital.
On Sunday, the Punjab law minister, Muhammad Basharat Raja, said at a news conference that intelligence agencies said Mr. Javed had had links to the Islamic State, and had been involved in abductions and killings.
Mr. Raja announced compensation of 20 million Pakistani rupees, or about $143,680, for the survivors of the shooting, and said an investigation would be completed within three days. He said the team that took part in the shooting and its supervisor were in police custody.
The authorities said that another police shooting, on Sunday, had killed two other men, whom they did not identify but said were linked to Mr. Javed. They described the men as terrorists who had been hiding in Mr. Javed’s house in Lahore and escaped after they learned of his killing.
The Pakistani authorities deny that the Islamic State has an organized presence in the country, but several militant networks here have expressed their support for the terrorist group.
As public furor over the police has increased, opposition political parties have sharply criticized Mr. Khan’s government. The Pakistan Muslim League-Nawaz has asked for a debate in Parliament about the shooting.
“The killings of parents in front of their children has exposed all tall claims of ‘good governance,’” said Bilawal Bhutto Zardari, the chairman of the Pakistan Peoples Party, another opposition party.
“The killings are a message to the people of the country that they should not go out with their children,” he said.