Authorities in Pakistan have hanged two convicted militants in the first executions following the reinstatement of the death penalty in the wake of this week's Peshawar school massacre.

Two officials and Pakistan's state television said the executions were carried out in the central city of Faisalabad.

There was no official confirmation of the executions.

Following the school massacre on Tuesday by Taliban militants, which saw 148 people killed, the government reinstated the death penalty on Wednesday.

Pakistani jets and ground forces earlier killed at least 77 militants in a north-western tribal region near the Afghan border.

A Pakistani prosecutor also said the government will try to cancel the bail granted to the main suspect in the 2008 Mumbai terror attacks - a decision that outraged neighbouring India and called into question Pakistan's commitment to fighting militancy.

The violence at a school in Pakistan's north-west earlier this week stunned the country and brought cries for retribution.

In the wake of the mass killing, the military struck targets in the Khyber tribal region and approved the death penalty for six convicted terrorists.

The military said its ground forces killed 10 militants on Thursday night while air strikes killed another 17, including an Uzbek commander.

Another 32 alleged terrorists were killed by security forces in an ambush in Tirah valley in Khyber on Friday as they headed towards the Afghan border, the military said.

On Friday morning, troops killed 18 more militants during a "cordon and search operation" in Khyber, the military said.

The military said the army chief, General Raheel Sharif, was travelling to Khyber to meet troops taking part in the ground operation.

Khyber is one of two main areas in the north-west where the military has been trying to root out militants in recent months.

Khyber borders Peshawar, where the school massacre happened, and militants have traditionally attacked the city before withdrawing to the tribal region where police cannot chase them.

The other area is North Waziristan, where the military launched a massive operation in June.

In the southern province of Baluchistan, Pakistani security forces killed a senior Pakistani Taliban leader along with seven of his associates in three separate pre-dawn raids, said a tribal police officer, Ali Ahmed.

On Thursday night, the Pakistani army chief signed the death warrants of six "hard core terrorists" convicted and sentenced to death by military courts, the army said.

Prime Minister Nawaz Sharif on Wednesday announced that he would lift a moratorium on executions in terrorism-related cases.

The lifting of the moratorium was aimed at demonstrating the government's resolve.

But the decision by an anti-terrorism court on Thursday to grant bail to the main suspect in the Mumbai attacks, Zaki-ur-Rahman Lakhvi, called into question that commitment.

Lakhvi is one of seven people on trial in Pakistan for the assault, but the trial has produced no results so far. It has been closed to the media.

India reacted with outrage to news of Lakhvi's pending release.

Special public prosecutor Abu Zar Peerzada said he would appeal to the High Court to cancel the bail and said Lakhvi had not yet been released.