Ashraf Ghani made the remarks during an address to parliament a week after a Taliban assault on the Afghan capital, Kabul, killed 64 people and wounded another 340.
Afghan officials have long accused Pakistan of turning a blind eye to the Taliban, the leadership of which is widely believed to be based in the Pakistani cities of Quetta and Peshawar, near the border.
Ghani said there are "no good or bad terrorists, they are just terrorists," and that "Pakistan must understand that and act against them," the Associated Press reported.
Afghanistan, Pakistan, China and the United States have been trying to revive peace talks between Kabul and the Taliban in recent months, but have made little progress.
"We don't expect Pakistan to bring the Taliban to the negotiating table," Ghani said. "What we want is for Pakistan, based on the four nations' agreement, to keep its promises and launch military operations against insurgents."
Pakistan has denied past allegations that it aid the Taliban and says its influence over the group has been overstated.
Pakistan has been waging a military offensive against militants in the North Waziristan tribal region since 2014, But critics have long accused it of fighting its own insurgents while covertly supporting groups that attack neighboring Afghanistan and India.