Officials said Arab and Palestinian figures had asked Meshaal to take on a fourth term as the movement's leader during a meeting of Hamas leaders with Egyptian intelligence chief Rafat Shehata Sunday and Monday in Cairo.
Meshaal said heading the Palestinian Liberation Organization was a possibility.
Hamas "hasn't made its final decision regarding the presidency. If Hamas nominated me to head the PLO, this is Hamas' natural right. But we're not going to fight for the presidency," he said.
Meanwhile, Hamas Prime Minister Ismail Haniyeh spoke with Shehata about a ceasefire with Israel in November that was breached, Hamas spokesman Taher al-Nunu said.
The two discussed accusations Hamas was involved in an attack near the Rafah border town in 2011, said the Hamas-affiliated Palestinian Information Center website.
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