Pakistan has bombed the fuel depot of private airline Kam Air near Afghanistan's Kandahar airport, the Taliban said on Friday, as the worst conflict in years between the South Asian neighbours flared again despite efforts to calm tensions.

The fighting erupted last month with Pakistani air strikes inside Afghanistan that Islamabad said targeted militant strongholds. Afghanistan called the strikes a violation of sovereignty as it launched retaliatory attacks.

"The company (Kam Air) supplies fuel to civilian airlines as well as to United Nations aircraft," Taliban spokesperson Zabihullah Mujahid said.

Pakistan also carried out bombings in other areas, including the capital Kabul, with women and children among those killed as civilian homes were targeted in some locations, he said, adding that the aggression would "not go unanswered".

Before the latest attack, neither side had reported any Pakistani air strikes on Afghanistan in recent days and ground fighting along the 2,600 km (1,600 mile) border had also tapered off.

Pakistan's military did not respond to a request for comment.

Militancy has been a bone of contention between allies-turned-foes Pakistan and Afghanistan, with Islamabad saying Kabul provides safe haven to militants executing attacks on Pakistan.

The Taliban, however, denies the allegation and says militancy is Pakistan's internal problem.

Reuters had reported on Thursday that mediation efforts by China, which had been urging an end to the violence, had helped ease the fighting between the countries.

Pakistan's foreign ministry spokesperson Tahir Andrabi had also said that Islamabad and Beijing were engaged in a "dialogue process" on Afghanistan.