"The infighting was between Wali ur Rehman and Hakimullah Meshud."
An intelligence officer in South Waziristan said he had reports that Hakimullah Mehsud died in the shooting after heated exchanges between the rivals at the meeting held around 4.30 pm local time (10:30 GMT).
"According to reports Wali-ur-Rehman fired and killed Hakimullah Mehsud," the official said.
Other reports suggested both men had died and a Taliban official denied that the incident had happened.
Al Jazeera's Kamal Hyder, reporting from Islamabad, said: "We're getting reports that the shura [council] was meeting in Makeen and there was a power struggle after which a gun battle ensued."
"We're getting reports that Hakimullah Mehsud and Wali-ur-Rehman were killed," he said, but stressed there was no independent verification.
A Taliban official in South Waziristan insisted that the government had fabricated reports of fighting between the different factions.
Noor Said, who has been a spokesman for the Pakistani Taliban in the past, said: "There was no fighting in the shura. Both Wali ur Rehman and Hakimullah are safe and sound."
The reports have added to earlier confusion surrounding the reported death of Baitullah Mehsud, the Pakistani Taliban leader who had a US bounty of $5m on his head.
There has been widespread speculation that Mehsud was killed, along with his wife and bodyguards, after a US drone aircraft fired missiles at his father-in-law's house in the village of Makeen earlier in the week.
But, earlier on Saturday, Hakimullah Mehsud told reporters by telephone that Baitullah Mehsud was in good health and would soon appear in the media to prove that he was alive.
Haikmullah Mehsud called the reports of Baitullah's death "black propaganda" aimed at luring the Pakistani Taliban leader into the open so that he could be targeted.
His claims were echoed by Maulana Merajuddin, who heads a delegation representing Mehsud's tribe in Islamabad.
"I believe that what we have heard by media sources during the past few days on the killing of Mehsud is incorrect," he told Al Jazeera.
"My sources from local citizens in Waziristan confirm that Mehsud is alive and doing well."
The reports of a shura, or meeting, to decide on succession within the Taliban have fuelled speculation that Baitullah Mehsud was indeed dead.
But there remains no physical evidence of Baitullah Mehsud's demise and previous claims of his death have proved false.