The two men disagree over control of the Palestinian security forces, a deadlock that is further hampering efforts to revive peace talks.
The Fatah Central Committee planned to meet again on Thursday in an attempt to resolve the dispute.
The deadlock has prevented Qurei from forming a new cabinet and resuming peace talks with Israel. A similar dispute led to the resignation of Qurei's predecessor, Mahmoud Abbas, after just four months in office.
According to a senior Palestinian official, Finance Minister Salam Fayad has added to the uncertainty by threatening to resign if Qurei does not stay on as premier.
Should Fayad leave, peace efforts will be dealt another serious blow. The former International Monetery Fund official is well-respected by American and Israeli negotiators.
Across in Israel, Prime Minister Ariel Sharon has been working on getting his cabinet to support a planned prisoner swap with the Lebanese guerilla group Hizb Allah.
Sharon's office said the prime minister would present the controversial deal to his cabinet for approval on Sunday. Under the arrangement Israel is expected to hand over more than 400 Lebanese and Palestinian prisoners in exchange for an Israeli businessman, Elhanan Tannenbaum, and the bodies of three soldiers.