Nadeem Aslam Chaudhry, the chief secretary of the Khyber Pakhtunkhwa province, told Reuters news agency Thursday's attack was "a major tragedy", with the death toll "likely to rise". At least 11 people were injured, he said.
Details of exactly what happened are still emerging, but Javed ullah Mehsud, a senior administration official, told AFP "approximately 10 attackers" were involved, "firing indiscriminately from both sides of the road".
Women and children had hidden in nearby houses, while police hunted for the attackers, he added.
Most the passengers travelling in the convoy through the mountainous area were Shia, he said in an earlier statement.
Sunni and Shiite Muslim tribes have clashed repeatedly this year. An earlier series of attacks ended after a tribal council called for a ceasefire, according to Reuters news agency.
Then last month, there was another attack on passenger vehicles along a road in the region which killed 15 people.
Sectarian violence is often linked to land disputes in the region.
However, Kurram, in Pakistan's north-west, also borders several Afghan provinces which are home to anti-Shia militant groups, including the Islamic State group and the Tehrik-e-Taliban Pakistan (TTP).