The South Asian nations show no signs of rapprochement in their worst fighting in years, adding to the volatility in a region also contending with US and Israeli strikes on Iran - a nation that borders both Afghanistan and Pakistan.
Combat has included Pakistani air strikes on Taliban government installations, such as the Bagram air base north of the Afghan capital Kabul.
Afghanistan's Ministry of Defence said Taliban forces struck Pakistani military installations in more than two dozen locations along the 2600-km border, destroying 14 posts and shooting down a drone.
It said seven Afghan civilians and three Taliban fighters were killed in overnight fighting.
Pakistani security sources said they carried out ground and air operations against military targets including Kandahar, the heartland of the Taliban and where its core leadership resides, and destroyed several Afghan border posts.
People living in border towns say troops begin exchanging heavy shelling after sunset, placing homes in the firing line just as families sit down to break their fast in the holy month of Ramadan.
The town was quiet on Friday, with only a few vehicles on the roads. Some homes were damaged from the fighting, and a cloud of black smoke could be seen across the border.
"The situation in Afghanistan and Pakistan remains tense amid active conflict along the border," the United Nations refugee agency said, adding that some 115,000 people in Afghanistan and 3000 in Pakistan were thought to have fled their homes.
Several countries have offered to negotiate a truce, most recently Turkey, although the Iran war has diverted the attention of most Gulf states that had stepped forward.
Pakistani government spokesperson Mosharraf Zaidi said no negotiations were taking place to end the conflict.
"There is nothing to talk about. There will be no dialogue and no negotiations," he told state-owned Pakistan TV.
"Terrorism from Afghanistan has to end - that is Afghanistan's problem. Pakistan's responsibility is to protect its citizens."
The conflict began last week with Pakistani air strikes inside Afghanistan that Islamabad said targeted militant strongholds. Afghanistan called the strikes a violation of sovereignty and announced retaliatory operations.
Islamabad has said Kabul provides safe haven to militants executing attacks on Pakistan from its soil. The Taliban has denied aiding such groups and said militancy in Pakistan is an internal problem.
Both sides have regularly said they inflicted heavy damage on the other and killed hundreds of opposition troops, without providing evidence.
The UN mission in Afghanistan has said 56 civilians have been killed and 128 wounded since fighting began. The Taliban government has said 110 civilians have been killed.
Pakistan has rejected both sets of figures, saying it targets only militants and support infrastructure.
