The operations, launched on Saturday night, were aimed at foiling attacks planned by the Taliban on Afghan forces, said a senior security official in capital Kabul, adding that clashes have escalated following the collapse of diplomatic talks between the U.S. and the Taliban.
The defense ministry in a statement said that the Taliban's designate governor for northern Samangan province, Mawlavi Nooruddin, was killed along with four fighters in an air strike in Dara-e-Soof Payeen district.
But the Taliban denied the governor had been killed.
"He (Nooruddin) is alive," said Zabihullah Mujahid, a Taliban spokesman said in a statement.
In a separate incident, Mullah Sayed Azim, a Taliban designate governor for Anar Dara district in western Farah was killed in a joint Afghan and foreign force raid.
"Sayed Azim was killed along with 34 other insurgents in Anar Dara," said Mohibullah Mohib, a spokesman for Farah provincial police.
Senior security officials in Kabul said several joint operations will be launched against Taliban and Islamic State fighters to prevent attacks on Afghan forces and civilians ahead of the presidential polls on Sept. 28.Fighting picked up in several parts of Afghanistan last week after U.S. President Donald Trump's abrupt cancellation of talks with the Taliban aimed at withdrawing U.S. troops and opening the way to end to 18 year-long war in Afghanistan. Last week the Taliban killed four Afghan special force members in a car bomb blast.