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.