Khalid Mehsood, deputy leader of the umbrella Tehreek-e-Taliban Pakistan (TTP), died after the pre-dawn strike in North Waziristan tribal agency on February 8, the militants said in the emailed statement. He added that a commander called Mufti Noor Wali Wali was appointed by the Taliban chief to succeed Sanja.
The militant group has not yet commented on the reported deaths.
Islamabad opposes the drone strikes, saying they violate its sovereignty.
Donald Trump's Afghanistan strategy will embroil the USA in a "perpetual war" that is doomed to fail, a senior Pakistani official has warned.
Washington has designated Sajna a global terrorist.
Recently, the terrorist attacks by the Taliban had increased in Afghanistan leading the USA to consider "unilateral steps in areas of divergence" to counter the militants.
The militant group has taken responsibility for numerous suicide bombings and other terrorist acts over the past decade in which tens of thousands of Pakistanis, including security forces, have lost their lives.
The deputy chief of the Pakistani Taliban has been killed in a United States drone strike, the militant group said in a statement Monday, as Washington continues to intensify attacks along the Afghan border region.
Sajna was believed to be residing in Khost and was returning to the Waziristan region with his fighters when the drone hit them, according to sources within his Mehsud tribe.
Spokesman Faisal said the two sides under the Afghanistan-Pakistan Action Plan for Peace and Solidarity engagement are discussing counterterrorism cooperation, repatriation of Afghan refugees from Pakistan, and ways to promote a peaceful settlement to the Afghan conflict.