"Eight policemen and four civilians have been killed since yesterday," Sami-Ul Haq Badar, an Afghan army general, said on Monday.
Despite the end to the army battles, reports have emerged that two US soldiers were killed on Monday in Pakistan's northwest Kurram region.
US and Pakistani army soldiers had met to discuss moves to bring a lasting end to the clashes between the armies of Afghanistan and Pakistan, according to an Afghan government spokesman.
"At the meeting, a Pakistani officer rose up and fired at US soldiers, resulting in the deaths of two soldiers and wounding of two others," Zahir Azimi, an Afghan defence ministry spokesman, told Reuters.
He said US soldiers had returned fire, killing several Pakistani troops.
Major General Waheed Arshad of the Pakistan army said it was unclear what had happened in the incident.
"We don't know who fired. We have ordered an inquiry. We have cordoned off the area," he said.
According to Afghan officials, Sunday's fighting erupted between after Pakistani forces took some areas in a border region in Paktia.
Pakistan said paramilitary forces retaliated after Afghan troops started "unprovoked firing" on border posts in the Kurram tribal region in northwest Pakistan.
Afghanistan said thousands of civilians joined government forces in fighting Pakistani troops after two Afghan children were killed.
Relations between the neighbours have deteriorated badly in recent months.
Afghanistan says Pakistan is not doing enough to stop Taliban insurgents operating from the Pakistani side of the disputed border.
Pakistan, the main backer of the Taliban before the September 11 attacks in the US, says the root of the Taliban problem is in Afghanistan.
Pakistan is building a fence along parts of the border, disputed since Pakistan's creation in 1947, in an attempt to stop infiltration by Taliban fighters.
Afghanistan opposes fencing a border it has never recognised.