Three police officers were killed by suicide attackers, but up to 27 insurgents were slain. Besides, a Taliban militant alleged to be behind the July kidnappings of 23 South Korean church workers was killed by police.
Mullah Mateen was among 16 militants killed in fighting late Monday and early Tuesday in Ghazni province, where the South Koreans were kidnapped, said Ghazni Deputy Gov. Kazim Allayar.
Two male hostages were killed early in the crisis, and two others, both female, were released last month. The remaining 19 were freed last week after direct talks between the Taliban and South Korean government representatives.
Allayar said Mateen played a key role in the kidnapping, including negotiating with the government in the early days of the kidnappings, which underscored the security problems facing Afghanistan at a time of surging Taliban violence.
He said another Taliban leader wanted over the kidnappings, Mullah Abdullah Jan, remained at large.
A Taliban spokesman said he was not able to comment on the claim of Mateen's death, which a senior police official also made.
Earlier, the U.S.led-coalition said in a statement its troops, along with Afghan forces, killed "several" militants overnight in the same part of Ghazni where Allayer said Mateen and the 15 others was killed.
The statement made no mention of Mateen and it was not immediately clear whether it was referring to the same battle.
The suicide attacks took place Tuesday in Kunduz town in northern Afghanistan and on Monday in Paktika province, a militant hotspot that borders Pakistan.
Officers in Kunduz had been trailing a suspicious vehicle before they challenged the driver as he neared the town's bus station, deputy police chief Mohammed Omar Khail said. As they opened the doors, he detonated his explosives, killing two officers and wounding five others, he said.
In the attack in Paktika, a suicide bomber rammed his vehicle into a police car, killing one officer and wounding two others, said Ghamia Khan, spokesman for the governor of Paktika.
Also Monday, a joint U.S.-led coalition patrol came under suspected Taliban attack in southern Kandahar province, a separate statement said. At the request of the ground forces, aircraft bombed the Taliban positions, killing "over one dozen" of the fighters, the statement said.
It was not possible to confirm casualty figures because travel to both areas is extremely dangerous.
The Taliban ruled most of Afghanistan from the mid-1990s until 2001, imposing an extreme version of Islam and harboring al-Qaida leaders and thousands of other Muslim militants from around the world.
They were ousted by a U.S.-led coalition following the Sept. 11, 2001, attacks in the United States, but are now leading an increasingly bloody insurgency. More than 4,200 people - most of them militants - have been killed so far this year, according to an Associated Press count.
The United States has imposed new sanctions against the Nord Stream 2 gas pipeline project, which still remains under construction