"I urge the Government and opposition commanders to issue clear instructions so that the message reaches across the country, down to the fighter and soldier at the local level," he told the Assembly members.
The UN estimates that more than 8,000 people, mostly civilians, have been killed, with another million people needing humanitarian relief inside the country, and tens of thousands displaced since the protests in Syria – part of the broader Arab Spring movement across North Africa and the Middle East – began in March last year.
Mr. Annan also voiced concern that violence has not abated and that alarming levels of casualties and abuses continues to be reported daily, although the Government had informed him of a partial troop pull-out from three locations – Idlib, Zabadani, and Deraa.
"I await further action and fuller information," he said. "The Government has indicated that it will continue to update me on steps it is taking. But it is clear that more far-reaching action is urgently required."
Mr. Annan told the Assembly that, as agreed with the Syrian authorities, a UN team, including officers from the Department of Peacekeeping Operations (DPKO), had arrived in the country to start technical preparations for the potential deployment of observers to monitor a cessation of armed violence and the full implementation of his six-point peace plan.
The six-point proposal, which was submitted during his visit to Damascus last month, seeks to stop the violence and the killing, give access to humanitarian agencies, release detainees, and kick-start an inclusive political dialogue.
"The violence in Syria cannot be addressed through the means of a traditional observer mission interposed between two armies," said Mr. Annan. "There is no established frontline. Peace will not be consolidated without a credible political process. What we would need on the ground is a small and nimble United Nations presence."
He also stressed the need to quickly move forward on a political process to meet the aspirations of the Syrian people. He urged the international community to remain united behind one mediation effort, which, he said, offered the best chance to end the violence and help the country steer its own course to a peaceful and democratic future.
Earlier, in their remarks to the General Assembly's meeting, Secretary-General Ban Ki-moon, and the President of the General Assembly, Nassir Abdulaziz Al-Nasser, urged the international community to continue supporting the envoy's initiative.
In his remarks, the Secretary-General noted with concern that bloodshed continues in Syria despite the Government's acceptance of Mr. Annan's proposal to end the violence.
"Despite the Syrian Government's acceptance of the Joint Special Envoy's plan of initial proposals to resolve the crisis, the violence and assaults in civilian areas have not stopped," Mr. Ban told the General Assembly meeting. "The situation on the ground continues to deteriorate."
"It is the responsibility now of the Syrian authorities to deliver on what they have promised, and to implement, fully and unconditionally, all the commitments they have given to Joint Special Envoy Annan," Mr. Ban added.
He appealed to Syria's President Bashar al-Assad, his Government and all concerned, to show "vision and leadership," and also urged the opposition to be ready to cease all violence, as outlined in Mr. Annan's plan.
"Beyond a cessation of violence, it is critical to move fast on the political process. A pause in hostilities will not hold without a political horizon," Mr. Ban said. "In this regard, the Syrian opposition is taking steps to present itself as a coherent body. This will be important for dialogue."
The Assembly's President, Mr. Al-Nasser, also stressed that it is essential that Mr. Assad implement Mr. Annan's plan immediately, ensuring that Damascus meets its commitment by the 10 April deadline.