Mehsud, flanked by other Taliban commanders in a show of unity, spoke to a small group of reporters, on the condition the interview only be published on Monday.
Mehsud said his group would avenge the killing of Baitullah Mehsud and hit back at Pakistan and the US for the increasing number of drone attacks in the tribal areas along the border with Afghanistan.
Unmanned drones have carried out more than 70 missile attacks in northwestern Pakistan over the last year in a covert programme, killing several Taliban commanders along with sympathisers and civilians.
The Pakistani government publicly condemns the attacks but is widely believed to sanction them and provide intelligence for at least some.
American officials have said they are considering a strategy of intensified drone attacks combined with the deployment of special operations forces against al-Qaeda and Taliban targets on the Pakistani side of the border.
As part of the offensive against the Taliban leadership, Mehsud's brother, Kalimullah, was killed last month.
Analysts say the group is struggling to regroup from the attacks on its leaders.