In a letter issued through social media, Umar Khalid Khurrasani, who heads the Mohmand tribal area wing of the TTP or the Tehrik-i-Taliban Pakistan, claimed to have killed 23 members of a paramilitary force, kidnapped in 2010, on Sunday at some unknown place in the region.
Dawn newspaper said the captives were killed to avenge what Khurrasani said was the killing of incarcerated Taliban fighters in various parts of Pakistan. The letter written in Urdu said the Taliban had warned against such killings of their activists.
Dawn said the Taliban faction's claim could not be independently confirmed.
The Dawn report quoted analysts as saying they believe the Mohmand group has not been in favor of the peace talks.
"We have warned the government time and again through the media to stop the killing of our friends, who were in the custody of security forces, but the government continued killing our people," the Washington Post quoted Khurassani's written statement as saying. "So we executed 23 members of the parliamentary" Frontier Corps.
The Post said the Pakistani Taliban, which have escalated their violence in recent months, have also killed dozens of captured or kidnapped Pakistani soldiers in the past.
The report said the Pakistani Frontier Corps, which is deployed mostly along the western border with Afghanistan, has suffered a number of casualties as it fights the Taliban insurgency.
The latest claim about the killings of the 23 security personnel, if confirmed, could be a setback for the government of Prime Minister Nawaz Sharif, which has opened talks with the TTP to end the uprising.
However, the TTP violence has continued since the talks began this month. A suicide bomber last week killed 12 police officers in Karachi, which was later claimed by the Taliban.
The government and the Taliban negotiators, however, have vowed to keep peace talks moving despite the insurgency, which has been going on for seven years.
Irafan Siddiqui, leading the government side, and Maulana Samiul Haq, speaking for the TTP, also have said they do not want the talks to languish, although there remains much skepticism among some experts whether the talks would produce lasting peace.
Sharif has said he is optimistic about the outcome, calling them a last chance to save the country from terrorism. He also said his government will not allow the country to be held hostage by them.
Prior to the offer to negotiate, there had also been rumors the government was considering a major military offensive against the militants. Some analysts have said Pakistan's new military chief has favored using force against the militants.
The government has said there should be a cease-fire before progress can be made at the peace talks, but the Post said the two sides have yet to agree on that.