Addressing the Council of Minister's meeting on Monday morning in Kabul, CEO Abdullah Abdullah condemned the overnight attack on border police by Pakistani forces but said a ceasefire had been agreed upon.
At least one Afghan border policeman was killed and six others injured in the clash, officials said earlier.
The clash started on Sunday night at about 9:15pm local time and continued for more than seven hours, executive officer of the border police forces, Mohammad Ayoub Hussainkhil said.
Hussainkhil said that the clash happened after Pakistan border police wanted to build installations at Torkham.
Abdullah said government and Pakistan had an agreement that before building any new installations in that area, they would be discussed and mutually agreed upon according to international law.
"We have discussed this through diplomatic channels too but Pakistan didn't act upon the decisions we had," he said.
"Pakistan wanted to build new installations and Afghan Border Forces didn't allow it. Pakistan went further and fired towards Afghan Forces," he added.
"One of our border soldiers was martyred and six others wounded in the clashes against Pakistan last night. The other side had casualties too."
He went on to praise Afghan security forces and said: "We have the right to protect ourselves and no one should look down at us when it comes to defending our sovereignty and integrity."
"We have proved that we are able to protect our homeland and our people. The current fight Pakistan started doesn't help anyone's interest."
He said: "We currently have agreed on a ceasefire with Pakistan. We hope this problem will end through the work by diplomatic addresses."
Abdullah also offered his sympathy to the "people and government of U.S for the tragic incident in Orlando, Florida," which killed 50 and wounded 53.
"This attack in Orlando is telling us that terrorism knows no religion, race, boundary and geography. Terrorism must be eliminated," he said.
He also said that they would discuss at Monday's meeting the issue of abductions in Kabul. "Security forces must take extra measures to avoid such cases in future," Abdullah said.
Meanwhile, Pakistani officials confirmed that two of their border policemen were injured in the Torkham clash.
This comes after Pakistani border police recently closed the border gate to Afghans without visas.
Officials said that the Torkham border is now closed after the attack.
A week ago, a number of vehicle drivers and shopkeepers in Torkham protested over the continued closure of the Torkham border.
The protestors said that Torkham is not recognized as the border between the two countries and Pakistan does not have the right to close the gate.
The protestors warned Pakistan that if they do not open the gate they will face a major response from Afghans.
Hundreds of Afghan travelers, many of whom are medical tourists, cross through Torkham daily.