Khost provincial governor spokesman Talib Mangal confirmed the incident, but said two Afghan civilians and four Pakistani troops were killed.
Kurram is one of the most sensitive tribal areas as it borders three Afghan provinces and at one point was one of the key routes for militant movement across the border.
Tribal elders reportedly made announcements at several mosques in the nearby areas, appealing tribesmen to join the security personnel on the border.
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The ISPR claimed that Pakistan expressed restraint following the attack on its troops. "Military engagement is under way to defuse situation", read the statement. Afghanistan does not recognize it as an worldwide border and has objected to new fortifications being built by Pakistan.
Initially, Afghan National Police interim chief Col. Abdul Hanan told Anadolu Agency an Afghan civilian was killed and two Pakistani troops were arrested during the clash.
The two countries are separated by the 2,400-kilometer (1,500-mile) Durand Line, which was drawn by British rulers in 1896. Clashes are still underway, Col Hanan said.
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He said the Afghan security forces have bodies of three Pakistani troops in custody and those would be handed over to Islamabad in accordance with the state-to-state and global protocols.
According to Azadi Radio, Pakistani forces are shelling Afghan border posts in Zazi Maiden.
Afghan officials often give conflicting casualty figures.
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The ISPR also accused Afghanistan of opening fire on Pakistani troops in the country's Kurram Agency when they were carrying out routine surveillance along the Pak-Afghan border and making necessary preparations for starting fencing of that area. Pakistan and Afghanistan share almost 2,600-kilometer, mostly porous, border and both sides routinely accuse each other of initiating cross-border skirmishes.