Ban floated the idea of deploying an international force to the UN Security Council on Wednesday, after the respective discussions with Abbas and Olmert.
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A senior member of the Organisation of the Islamic Conference (OIC), the world's main Muslim body, also rejected the deployment of an international force.
"What is needed is not external forces. What is needed is a better understanding between internal forces," Ekmeleddin Ihsanoglu, the OIC's secretary-general, said in Kuala Lumpur.
Ihsanoglu said he has appealed to Palestinian leaders to show a deeper strength of leadership.
"The situation cannot be allowed to further deteriorate. There is a need for strong leadership on behalf of all political leaders," he said.
Hamas fighters appear to be winning control of key areas in the Gaza Strip.
A victory for Hamas in a Gaza could ultimately divide Palestinian civilians between a Hamas-controlled Gaza and a Fatah-run West Bank.
Such a factional rupture would further threaten the prospect of an internationally recognised Palestinian state.