The meeting was organized by the PLO's Culture and Media department and included Executive Committee member Hanan Ashrawi as a panelist.
The rival Hamas and Fatah officials disagreed on the success of reconciliation efforts, with al-Ahmad claiming that reconciliation had come "very close" and Dweik stating that "no tangible breakthrough" had been made.
Both officials tried to undermine the achievements of their rival faction, with Dweik claiming Fatah had begun as as armed resistance faction but was now coordinating on security with Israel.
The Hamas official lauded the resistance achievements of the Islamist group, noting the group's ability to launch rockets at Tel Aviv in fighting last November.
At that point Hamas officials withdrew from the meeting.
In the aftermath, Fatah spokesman Ahmad Assaf said that "Dweik has offended the Palestinian people, their history, their martyrs and their security services while trying to justify the coup and the killings in the Gaza Strip."
Ashrawi, who was sitting between both officials, said she was surprised by Dweik's comments.
"The panelists have not criticized Islamist leaders, neither has the panel focused on religion, and for that reason we were deeply surprised when religion was introduced during the panel," she said.
Hamas' Change and Reform bloc in turn responded by criticizing al-Ahmad's comments about Dweik, saying they "reflect a state of immorality which went far beyond political rivalry and boosting the occupation's support."
Hamas-affiliated lawmaker Marwan Abu Ras called for Fatah to replace al-Ahmad as their PLC speaker, claiming that the official was trying to deepen the state of disagreement between factions and maintain internal rivalries.
"His positions are harmful for Palestinian society and rather in line with the Zionist and American plots against resistance and against freedoms in the West Bank," he added.
Palestinian officials said recently that reconciliation meetings in Cairo had fallen short of expectations, with some questioning whether either faction had the will to end the political division.
A deal was signed in May 2011 to reunite the West Bank and Gaza, but political factions have repeatedly failed to reach an agreement concerning its practical implementation.