But he also reiterated Hamas was ready to discuss a "comprehensive" cease-fire with Israel.
"All Palestinian factions of resistance have expressed full readiness to deal with the issue of calm, on condition that it be comprehensive, reciprocal and simultaneous," Meshal was quoted as saying.
The Gaza-based Web site also said Meshal wrote to Arab leaders requesting support for Hamas-Fatah dialogue, after a Yemen-brokered agreement to revive talks between the rival factions appeared to falter this week.
Meshal, along with Hamas Prime Minister Ismail Haniyeh, urged Arab leaders to back the Yemen proposal for Palestinian reconciliation.
Hamas and Fatah have been at loggerheads since the breakdown of a unity Palestinian government last year, culminating in Hamas seizing control of the Gaza Strip after days of bloody internecine violence.
Members of the Arab world are meeting this weekend in Damascus, although many Arab leaders are skipping the event, sending instead lower ranking officials and highlighting the rift between pro-U.S. states and Iran and Syria.
Meshal called on Arab leaders to "shoulder your national and brotherly responsibility to foster a Palestinian-Palestinian dialogue", according to the report, which was also carried by London-based pan-Arab newspaper al-Hayat.
In a televised speech to the Arab summit, Haniyeh urged Arab leaders to endorse the Yemeni initiative, despite what he said were American and Israeli objections.
"We hope you don't allow any external interference in the way of reconciliation," he said. "Our people would judge the success or failure of the summit in Damascus on how seriously it deals with the lifting of the siege on Gaza."
Hamas has said any cease-fire would depend on an end to Israeli acts of "aggression" in Gaza and the West Bank and the reopening of Gaza border crossings.
Egypt, with U.S. blessing, has been trying to broker a cessation of hostilities between Israel and militants in Gaza.
Israel, denying it is involved in cease-fire negotiations says it would have no reason to strike Hamas if rocket salvoes ceased.
Meanwhile, Hamas members in the Gaza Strip on Friday called on Arab states to drop their proposal for a comprehensive peace deal with Israel, and support the militant group's policy of violence.
On Thursday, Arab foreign ministers re-endorsed the Saudi plan for peace with Israel originally launched in 2002.
About 2,000 people gathered at a Hamas-organized rally in Gaza, as delegates convened in Damascus ahead of the annual Arab summit. Hamas was not invited to the summit hosted by its closest ally in the region.
Hamas official Khalil al-Haya said Israel would only respond to violence, and encouraged others to join it.
"Cut all ties with Israel, withdraw the Arab initiative," he shouted. "The Zionist enemy doesn't have a vision of peace. Only force ... fighting and holy war works with [Israel.]"
The Saudi-sponsored peace initiative offers Israel peace with all Arab countries in return for withdrawal from all the lands it captured in the 1967 Six-Day War, the creation of a Palestinian state with a Jerusalem as its capital and a solution to the refugee issue.
Mushir al-Masri, another Hamas official, said the Arab initiative was a burden on Palestinians. "Hamas is defending the honor and dignity of this nation on the [Arabs'] behalf," he said.
The rally was peppered with pleas from children for a lifting of the closure imposed on Gaza after Hamas violently seized the territory. "Your summit will be useless if you don't lift the siege on Gaza," a young boy screamed into a microphone.
Jordan, Iraq and Yemen, along with Egypt and Saudi Arabia, announced that their top leaders would not attend this weekend's summit. The annual summit is frequently plagued by no-shows. But this year, pro-U.S. nations are deeply embittered with hard-line Syria, over its meddling in Lebanese affairs and support of Palestinian Islamic militant groups.