The former UN chief briefed the powerful 15-member UNSC in a closed session by video-conference from Geneva on the latest developments concerning Syria and his efforts to address the crisis in the country.
He asked the Council to support the April 10 deadline and begin consideration of a potential UN monitoring mission to Syria.
Later talking to reporters, US Ambassador to the UN Susan Rice said Annan has pressed the Syrian government to cease troop movements, use of heavy weapons and pull out of troops from population centres by April 10.
Annan told the UNSC that the Syrian foreign minister sent him a letter on Sunday, in which he said that the Syrian military will begin immediately and will complete by April 10 "the cessation of all forward deployment and use of heavy weapons and will complete its withdrawal from population centers," Rice, who is the current President of the UNSC, said.
Annan urged the government of Syria to start implementing the withdrawal plans immediately and to ensure that forces move no further into population centers.
Rice said while the Syrian government has not put any "conditions or preconditions" to begin implementing Annan`s peace plan, she cautioned that "over the course of the last many months promises (have been) made and promises broken."
"We have seen commitments to end the violence followed by massive intensification of violence," she said, adding that the proof will lie in actions, not in words.
Rice expressed hope that unlike in the past, there would not be any escalation of the violence in Syria.
"We hope that the Syrian authorities will implement fully the commitments that they have made without any conditions or codicils, and should they do so, we will expect the opposition to follow suit within 48 hours, as specified by Joint Special Envoy Annan," the American envoy to the UN said.
The UN envoy is expecting details from the Syrian government "very shortly" on other aspects of his six-point peace plan, including requests for humanitarian access, two-hour daily humanitarian pause, access for the media and start of a political dialogue process.
Annan`s deputy Nassar al-Qidwa also has had "constructive exchanges" with the Syrian opposition to urge them to cease their operations within 48 hours of a complete cessation of government hostilities, Rice said.
A team, which will include some of Annan`s staff members, will travel to Syria this week to continue preparations for a potential monitoring and supervisory mission of the UN.
Rice said Security Council members expressed full support for Annan`s proposals, calling for his Six-point Plan to be implemented immediately, including a political process leading to a transition that meets the aspirations of the Syrian people for democracy.
While some Council members expressed concern over the Syrian government using the next few days to intensify violence, they overall expressed a willingness to consider Annan`s plan for a monitoring mission in case a cessation of violence is achieved.
Bashar Jaafari, Syria`s UN envoy confirmed that the April 10 date had been agreed "by common accord" between Annan and his government.
Annan was in Damascus recently to meet embattled President Assad for talks and has since been in contact with the Syrian government to demand that it start moves to halt the violence.
At a `Friends of Syria` meeting in Istanbul on Sunday, Arab, Western and other nations called for a deadline to be set, but Russia, Syria`s last major ally and a permanent member of the Security Council, has rejected the calls.
The UN estimates that more than 9,000 people have been killed in Syria in the year long uprising.