Both the Army and supporters of the Pashtun Tahaffuz Movement (PTM), which campaigns for the rights of ethnic Pashtuns in the former tribal areas bordering Afghanistan, accuse the other of initiating a clash at a military checkpoint at Khar Kamar.
In addition to the deaths, several people, including soldiers, were injured.
"The uncertainty surrounding the deaths at Khar Kamar requires a prompt, transparent and impartial investigation by Pakistani authorities," said Brad Adams, Asia director at Human Rights Watch.
"Upholding the rule of law is critical for maintaining security and protecting human rights in North Waziristan."
The incident arose during a protest at the checkpoint by local residents following the arrest of two men after a military search operation.
The search operation was in response to two attacks on Army personnel, on May 6 and May 24, that killed one soldier and injured three others.
A key PTM leader, Mohsin Dawar, told the media that as the group's elected representative, he and his supporters had gone to meet the demonstrators at the checkpoint. Dawar said that while he was meeting with the protesters, soldiers opened fire without provocation.
After the incident, the Army issued a statement that a group led by Dawar and Ali Wazir, another leader of the Pashtun group, attacked the military checkpoint to force the release of a suspected terrorist facilitator.
"In exchange of fire," the statement said, "three individuals who attacked the post lost their lives and 10 got injured."
The Prime Minister's Office endorsed the military's statement.
( With inputs from IANS )