Syria’s foreign minister wrote to Mr Annan, agreeing to the 10 April deadline, US ambassador to the United Nations Susan Rice said.
Mr Annan urged the Syrian government to start the withdrawal immediately and move no further into populated areas, and said that “commitment was provided”.
Syria’s ambassador to the UN Bashar Ja’fari said the deadline was set “by common accord” between Mr Annan and the Syrian government.
He also reiterated his government’s complete support for Mr Annan’s six-point plan to end the year-long Syrian crisis.
But Ms Rice, also the current UN Security Council president, expressed scepticism about Syria’s commitment, saying that Damascus has made and broken promises over many months.
She said: “We have seen commitments to end the violence followed by massive intensifications of violence.
“So the United States, for one, would look at these commitments and say, yet again, the proof is the actions, not in the words.”
Mr Annan’s plan to end Syria’s crisis calls for an immediate withdrawal of troops and heavy military equipment from populated areas, followed by an overall cease-fire – first by government forces and then by opposition fighters – to pave the way for talks by all Syrian parties on a political solution.
It includes an immediate daily two-hour halt to fighting so humanitarian aid can reach suffering civilians, and unhindered access for humanitarian groups and the media.