Annan briefed the 15-member UN Security Council on the "deeply dismaying reports of renewed fighting, particularly in North Darfur".
He said: "Thousands of Sudan armed forces have been deployed to the area, in clear violation of the Darfur Peace Agreement. Even worse, the area has been subjected to renewed aerial bombing.
"I strongly condemn this escalation. The government should stop its offensive immediately."
The Darfur Peace Agreement was signed in Nigeria last May by Khartoum and the main Darfur rebel movement. Two other rebel groups have refused to sign the deal.
Annan said that humanitarian workers in the country continue to be the targets of "brutal violence, physical harassment and rhetorical vilification" and that the humanitarian gains of the past two years "are being rolled back".
More than 3 million Darfuris are dependent on aid in the region which is the size of France. More than 14,000 aid workers are in the country, the world's largest aid operation.
Kenro Oshidari, head of the WFP in Sudan, said most of the 350,000 people cut off from food aid have gone three months without help.
He said: "Their situation is even more desperate because we're in the middle of the hunger season."
Memories of Rwanda
In his speech, Annan evoked the 1994 genocide in Rwanda: "Can the international community, having not done enough for the people of Rwanda in their time of need, just watch as this tragedy deepens?
"This is no time for the middle ground of half-measures or further debate."
Yasir Abdelsalam, Sudan's envoy to the UN, said that Khartoum was adhering to the May peace deal.
He accused the council of choosing "the path of confrontation" by adopting a resolution last month which was meant to speed up the transfer of authority over the peacekeepers to the UN.
But he also said that his government was ready to talk, something that diplomats said they believed was a good sign.
The UN wants to take control of peacekeeping in Sudan because the 7,000-strong African Union force is understaffed, starved of cash and has been unable to halt the violence in Darfur.
However, Sudan has said it would expel the AU peacekeepers if they insist on transferring their mission to the UN after an AU mandate expires at the end of the month.