"Eight policemen and four civilians have been killed since yesterday," Sami-Ul Haq Badar, Afghan army general, said on Monday.
Reports have emerged that three US and two Pakistani troops were wounded by gunfire at the border on Monday, shortly after they met Monday in Pakistan's northwest Kurram region to discuss a lasting end to the army clashes.
"The firing came from the Afghan side. Three American and two Pakistani soldiers were wounded," a Pakistani official said on condition of anonymity.
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 sharply 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.