Fatah, which is headed by Mahmoud Abbas, the Palestinian president, and officials from the ruling Hamas faction offered different accounts of the incident which occurred despite predictions by Hamas members that a joint government deal with Fatah was near.
Kibha told Reuters that Fatah gunmen had stopped his car at a makeshift checkpoint outside Tubas.
His convoy turned around and headed in the opposite direction, towards the West Bank town of Jenin.
A Fatah official said their gunmen had opened fire only after armed members of a Hamas-led police force accompanying the minister's car had shot towards them.
A Palestinian photographer was injured by a bullet fragment in the head, the official said.
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Hamas denies it has any police in the West Bank. Fatah has accused Hamas of seeking to build such a force there.
Disagreement over the Hamas police force in Gaza is a major obstacle to the sides wrapping up talks over a unity government.
After Saudi mediation, Hamas and Fatah agreed a month ago to forge a joint coalition cabinet, largely ending weeks of bloody factional fighting centred in the Gaza Strip in which more than 90 people were killed.
Abbas said on Thursday a unity deal was "99 per cent" agreed although he had not yet agreed with Ismail Haniyeh, the Hamas-aligned prime minister designate, who would be interior minister - a post that controls the powerful security services.
Saeed Seyam, the current interior minister from Hamas, said the movement has demanded its police force remain intact under any unity deal, pending a reorganisation of the other security forces now dominated by Abbas's Fatah.
Seyam, in Gaza, said: "The executive force will remain until the other security services are restructured."