Annan said all hostilities between the Syrian government and opposition forces must end by Thursday morning.
"We still have time between now and the 12th to stop the violence and I appeal to all concerned, the government in the first place, and the opposition forces," Annan said at a news conference in Istanbul, Turkey.
The Syrian government last week had agreed to withdraw troops by April 10 as part of Annan's six-point peace plan. White House press secretary Jay Carney said Tuesday there was no evidence of an end to the regime's aggression.
"Leaders of the Assad regime say a lot of things, make a lot of promises," Carney said. "Those promises, overwhelmingly, turned out to be empty. We judge, and the international community judges, the actions of the Assad regime, not their words. We have seen no evidence thus far of any pullback. We have seen much evidence of further brutality and aggression against innocent civilians."
Fighting was reported in several cities, opposition groups said Tuesday, as Annan visited a refugee camp in Hatay province in southern Turkey a day after Syrian forces fired across the border near a refugee camp, killing two Syrian refugees and wounding at least 23 other people, including a Turkish police officer and another Turkish citizen. Lebanon called on Syria to investigate the shooting death of a cameraman who was reporting on the unrest from the Lebanese side of the border.
"I believe it's a bit too early to say that the plan has failed," Annan said. "The plan is still on the table and it's a plan we are all fighting to implement."
Annan said there have been indications of government troops withdrawing in some areas but he expressed concern over reports of violence in other areas. The Local Co-ordination Committees reported 65 people died Tuesday in attacks in the Aleppo area. The opposition Syrian National Council umbrella group said 1,000 people had died in the last eight days, The Guardian newspaper in Britain reported.
The UN High Commissioner for Refugees told reporters in Geneva it was sending a team to assist at nine refugee camps on the border between Turkey and Syria. Spokesman Adrian Edwards said a plane carrying 1,600 tents and 1,400 blankets has been dispatched to the camps.
The United Nations said there are more than 25,000 registered Syrian refugees in Turkey, as well as 10,112 in Lebanon, 7,021 in Jordan and 792 in Iraq.
The Syrian National Council said it was ready to respect a cease-fire.
"The opposition, including the Free Syrian Army, says it will comply if the regime does," council executive committee member Bassma Kodmani was quoted by The New York Times as saying.
But she said the regime's actions were "clearly not a sign of their intention to cooperate in good faith."
Damascus said Sunday it would not honor the cease-fire worked out by Annan until it received written guarantees from rebel groups that they would stop fighting and written assurances from Qatar, Saudi Arabia and Turkey they would "stop funding and arming terrorist groups."