Sheikh Khalid Haqqani, who served on the group’s consultative council and had been a deputy leader, had been killed January 31.
The Pakistani Taliban key leader and another member of the group were killed in a clash with security forces in Afghanistan.
Afghan security forces declined to comment, and it was not immediately clear what type of mission Haqqani may have been on.
Both Islamabad and Kabul have long accused each other of allowing militants to shelter in the border regions and launch bloody attacks that threaten regional stability.
“Haqqani, also a writer of several books on different topics, was known for giving a befitting reply to so-called torch-bearers of democracy,” the TTP said in its statement.
Pakistan has been battling an inner Islamist insurgency for over a decade, with thousands of civilians and security personnel dying in extremist attacks, especially after the TTP began their campaign of violence in 2007.
But overall levels of extremist-linked violence dropped dramatically last year, with 2019 seeing the fewest deaths since 2007, the year the Pakistani Taliban umbrella group was formed.