Key Taliban commander killed

• Security forces: At least five militants and two suspected militants are killed Saturday


• The Taliban insurgents are killed in and around Peshawar


• Taliban gunmen killed 145 people, including 132 children, at a school in Peshawar

Peshawar, Pakistan (CNN) -- Pakistani security forces said they killed several Taliban insurgents in and around Peshawar on Saturday, four days after Taliban gunmen massacred scores of children the northwestern city.

At least five militants, including a key commander, were killed Saturday in a battle between security forces and militants in the Mattani area of Peshawar, sources said.

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In addition, at least two suspected militants and two police officers were killed in Charsadda, a suburb of Peshawar, sources said.

On Friday, the Pakistani military said it killed 32 militants in Khyber Pakhtunkhwa province, of which Peshawar is the capital. A military statement didn't specify whether any of those killed were Taliban members or whether the ambush was linked to Tuesday's deadly school attack, in which 145 people, including 132 children, were killed.

The school massacre prompted widespread revulsion across Pakistan. Prime Minister Nawaz Sharif responded by announcing an end to a moratorium on the death penalty in terrorism cases.

The Pakistani Taliban, known as the Tehreek-e-Taliban Pakistan, said they targeted a school, which mostly admits soldiers' children, because the students aspired to follow in their fathers' footsteps and target militants.

They also said it was revenge for the killing of hundreds of innocent tribesmen and their children during a recent offensive by Pakistan's military.

The Pakistani army has been conducting a ground offensive aimed at clearing out Taliban and other militants in the loosely governed tribal areas of northwestern Pakistan. The campaign has displaced tens of thousands of people.

The Pakistani Taliban, which have close ties with their namesake in Afghanistan, have long taken credit for an extensive list of assaults on civilians and security forces in Pakistan.

The attack on schoolchildren, however, was repellent even in the eyes of other militant groups in the region.

A spokesman for the Afghan Taliban condemned the Peshawar school attack because it involved the "deliberate killing of innocent people, women and children."

Osama Mehmood, a spokesman for al Qaeda's affiliate in India, similarly condemned the attack, blasting it as being against Sharia, or Islamic law.

"Our hearts are tearing apart with pain at the killing of innocent children," he said in a statement.

"The fighters of al Qaeda in the Indian Subcontinent condole the death of these children. Our target is not innocent civilians, women and children, instead we are responsible for their protection."

Zahir Shah reported from Peshawar, and Holly Yan wrote from Atlanta. CNN's Sophia Saifi and Jethro Mullen contributed to this report.