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Assad warned that once the conflict spills over into neighboring countries, blurring borders, that would set off a domino effect.
"Nobody can imagine how the region would look like in case of a redrawing of the map. That will be a map for uncounted wars in the Middle East and possibly elsewhere, that nobody can stop," he said.
The Palestinian militant group Hamas on Monday urged Hezbollah to withdraw its fighters from Syria and accused it of stoking sectarian tensions, in unprecedented public criticism against its former ally.
In a statement, Hamas, a Sunni movement, called on Hezbollah to "withdraw its forces from Syria and keep its weapons directed at the Zionist enemy (Israel)." Hamas also said that sending forces to Syria "contributed to the sectarian polarization in the region."
The Hamas statement came as the region's Sunni and Shiite Muslims are lining up on opposite sides of Syria's civil war.
The fall of Qusair shifted the balance of power on the battlefield in favor of the Damascus regime, which is now looking to keep the momentum and aims to take back control of Aleppo, the country's commercial hub. The rebels captured parts of the city last summer during an offensive in the north along the border with Turkey.
Troops clashed with rebels inside Aleppo and in the city's outskirts on Monday, activists said.
In addition to arming the rebels, Washington has also been contemplating other options, including imposing a no-fly zone over Syria, though no decision has been made.
Assad's air force has been his most lethal weapon, relying on it to prevent rebels from holding on to territory won on the ground.
A spokesman for Russia's Foreign Ministry, Alexander Lukashevich, said in a televised news conference Monday that "there are no conditions and no need for a no-fly zone" in Syria, adding that such measures by the U.S. and other would be "counterproductive."
The host of the G-8 meeting, British Prime Minister David Cameron, conceded Monday there is a disagreement on Syria, but said Russia, like all G-8 governments, has a responsibility to push opposing factions in the civil war to the negotiating table as rapidly as possible and not to back a government that "butchers" its citizens.
Russia supplies Assad's army with weapons and has its only Mediterranean port in Syria.
In a related economic development, the Syrian pound tumbled to a new low on Monday, diving from 170 pounds a dollar to 210 in a single day.
Syrian Prime Minister Wael al-Halqi rushed to calm nerves, saying the government has large reserves of foreign exchange and would put in place a package of economic measures to enhance the economy.
The premier referred to the support of "friendly countries," including Iran, citing its willingness to finance Syrian imports and requirements of the industrial and agricultural production.
The governor of the central bank of Syria, Adib Mayaleh, told reporters that the bank would continue its policy of intervention to prop up the value of the pound.