KABUL—Afghan President Hamid Karzai Saturday suggested that the Taliban should turn their weapons against Pakistan, escalating tensions with Islamabad days after the two countries exchanged fire along a disputed border.

Speaking to reporters in Kabul, Mr. Karzai praised an Afghan policeman who died in Wednesday's border clash and then called on the Taliban to "target the place that is hostile to Afghanistan."

No Afghan government, he added, will recognize as an international frontier the British-drawn boundary with Pakistan, known as the Durand Line, which cuts in two the ethnic Pashtun homeland.

Mr. Karzai's comments—his strongest remarks yet since the border clashes—may complicate U.S.-led efforts to mediate a peace settlement and to ship military equipment out of Afghanistan through Pakistan as most international troops prepare to leave the country by the end of 2014.

"Without cooperation with Pakistan, we will never be able to reach stability in Afghanistan," cautioned Haroun Mir, a Kabul-based political analyst. "We need their assistance for negotiations with the Taliban but we also depend on them for our economy."