At least seven people die in the sixth suicide bombing in Kandahar in nine days.
Authorities have not recovered Wali’s body, he said.
Nato has said it was not aware of Wali’s reported killing.
Several Taliban sources in Kandahar said 13 militants died in the attack.
The Taliban are mostly active in southern and eastern Afghanistan close to the border with Pakistan which they use as a haven.
Nearly 4,000 people have died in fighting this year, the bloodiest period since US-led forces overthrew the Taliban in 2001.
On Sunday, a suicide bomber rammed his car into a convoy of foreign troops in the southeastern province of Khost, killing a local civilian and wounding three others, police said. There were no casualties among the soldiers.