Kabul, in turn, has already accused Islamabad of carrying out unprovoked attacks in which civilians were killed – although Pakistan says it only targets militants.
The two countries agreed to a ceasefire last October following weeks of deadly clashes. However, as with internationally mediated truce agreements, this ceasefire has since collapsed.
The BBC has not independently confirmed the number of casualties claimed by the Pakistani and Taliban governments in the latest attacks.
The Afghan Taliban government says the strikes hit civilian homes, while Pakistan says they targeted militant hideouts in Afghanistan’s Paktia, Paktika and Kunar provinces.
The casualties were concentrated in Mandokhail, a village in Paktika province, according to Taliban officials.
Sunday’s attacks come a day after three members of the Sindh Rangers, a Pakistani paramilitary force, were killed at their headquarters in Karachi, according to the Pakistani military. Three militants also died in the suicide attack and Pakistani authorities said they had arrested a fourth, who was Afghan.
Jamaat-ul-Ahrar, a splinter faction of the TTP, claimed responsibility for Saturday’s attack.
The TTP, also known as the Pakistani Taliban, and Jamaat-ul-Ahrar are banned in Pakistan and by the United Nations due to their involvement in past attacks.
Intermittent border clashes and airstrikes in the border area have killed dozens of people in recent months, according to officials from both countries.
In February, clashes between the two countries left dozens dead. In March, a Pakistani strike at drug rehabilitation center in Kabul, hundreds of people were killed.
In early June, Pakistan launched deadly airstrikes that killed 26 militants. The Afghan Taliban government said 13 people, mostly children, were also killed in the strikes.