Annan warned Sudan’s leaders they could be held personally responsible for what was happening in the region if international troops were refused entry into the country.
Earlier the UN refugee chief warned of an impending "catastrophe". Antonio Guterres told how increasing violence in Darfur was now threatening the entire region.
Three years of conflict have left millions displaced and thousands dead. In addition, the UN reports that the situation shows no signs of improving, and aid agencies say it is actually getting worse as time goes by.
The African Union has given an announcement that it will pull out its 7,000-strong peacekeeping force next month, but Sudan has adamantly refused permission for a UN force to enter to replace it.
Annan said continuing to block UN intervention could leave Sudan's leaders open to be "held collectively and individually responsible for what happens to the population in Darfur".
A UN Security Council meeting on Monday will bring the situation in the country to the forefront of the debate.
A peace deal was signed in May between the government and the largest of the rebel groups, however, rather than solving the problems in the region, the violence has actually increased dramatically.
Especially worrying is that attacks on aid workers are an almost daily incident nowadays, with 12 having been killed in the last three months.
Speaking in Geneva, Antonio Guterres, the head of UNHCR, said it was a situation which could not continue. He said, "I think we are facing a terrible disaster. War is starting again, violations of human rights are massive, situations of rape - these have all kinds of devastating forms of impact in the lives of this population and make us feel more and more uncomfortable because we are not able to help them.
"We cannot even have access to them. This is unacceptable, this has to stop."
Various aid agencies have stated their belief that their work will be impossible without an international peacekeeping force present in Darfur.