The ministry said it was part of its effort to implement the UN's six-point peace plan.
The cease-fire is part of a six-point peace plan laid out by U.N.
The text of the draft calls for the immediate implementation of a six-point peace plan, as put forward by U.N.
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Last week the UN decided against extending the mission, which was originally part of a six-point peace plan for Syria.
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Secretary-General Kofi Annan, now the United Nations and Arab League joint special envoy to Syria, brokered a six-point peace plan in March.
He championed a six-point peace plan that has failed to take hold.
Annan's six-point peace plan also calls for a halt in violence by both sides and a Syrian-led political process to end the crisis.
The mission's job is to monitor U.N. and Arab League joint special envoy Kofi Annan's six-point peace plan that never got off the ground.
The resolution calls on Syrian government forces to withdraw from towns and cities, a key element in the six-point peace plan of joint U.N.
There have been calls for more action to be taken in Syria to stop the violence, which has continued despite Mr Annan's six-point peace plan.
The failure of Annan's six-point peace plan has emboldened opposition groups.
The cease-fire went into effect April 12 and is part of a six-point peace plan negotiated by U.N. and Arab League joint special envoy Kofi Annan.
It has authorized up to 300 monitors in Syria to monitor a cease-fire and the six-point peace plan of U.N. and Arab League envoy Kofi Annan.
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Meanwhile, the mandate of the U.N. observer mission that had been tasked to monitor Annan's six-point peace plan, which included a failed ceasefire, ends on Sunday.
Last month, the United Nations wound up the observer mission that had been tasked with monitoring the ceasefire in Syria under the six-point peace plan negotiated by Mr Annan.
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The Western powers are pushing for tougher action while Damascus's allies, Russia and China, say Mr Annan's six-point peace plan, which the Syrian government has agreed to, is sufficient.
The Obama administration said Syria had reached a "critical juncture" and again urged President Bashar al-Assad to uphold its commitment to the six-point peace plan brokered by special envoy Kofi Annan.
Kofi Annan, the joint UN-Arab League envoy and sponsor of a six-point peace plan, flew to Damascus to plead with President Bashar Assad to uphold the ceasefire ostensibly in place since April.
The U.N. and Arab League special envoy to Syria, Annan is visiting leaders in the region to find ways to implement his six-point peace plan, an initiative that has yet to gain traction.
Mr Fawzi said the former UN secretary general's six-point peace plan had so far been "relatively respected" by both the government and armed opposition, but that he was "aware that we don't have a perfect situation".
International diplomat Kofi Annan's six-point peace plan "failed from day one and is now meaningless for the Syrian people, " Riyadh al-Shaqfa, leader of the opposition Syrian Muslim Brotherhood party, said in a speech at a party conference in Istanbul on Monday.
There has also been no significant release of detainees and no substantive progress on providing humanitarian assistance, another point of the peace plan, Ban said.
CNN: U.N. Security Council to vote on Syria observer mission
So while then-prime minister Ehud Barak for instance claimed that his offer to cede the Temple Mount was contingent on the signing of a peace treaty, when the so-called Middle East Quartet issued its road map plan for peace, Barak's ostensibly canceled offer was the starting point of negotiations.
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