“Yes, we have carried out this attack. I will give details later,” Baitullah Mehsud said on the phone to the Reuters news agency.
Pakistani security forces took back with difficulty the police training school in Lahore after militants barricaded themselves inside, killing at least eight cadets and wounding many more.
Security officials are interrogating at least four suspects captured after the attack.
In a possible reference to Pakistan's long-time foe, India, Pakistani Interior Minister Rehman Malik suggested that a foreign state may have been involved.
For their part Indian authorities have condemned the attack on Lahore.
A few hours ago, another Pakistani Taliban, Omar Farooq, acting as the spokesman for little-known Fedayeen al-Islam, claimed responsibility for a similar attack in Lahore against the Sri Lankan cricket team earlier this month.
The Pakistan Taliban is linked to al-Qaida and Afghan Taliban militants based in the same cross-border area with Afghanistan.
Farooq threatened further attacks if the Pakistani government does not pull Pakistani troops out of Waziristan, or if the US and NATO do not stop their attacks and their leader, Maulana Abdul Aziz, is not released.
Aziz, who taught young people how to talibanise Pakistan, was the chief cleric at Islamabad's Red Mosque, which was the site of a pitched battle between militants and security forces in 2007.
The Lahore attack and the claims by Pakistan Taliban come a few days after the United States pledged further assistance to Pakistan against the militants and their “safe havens” in Pakistan's north-west tribal region bordering Afghanistan.