Annan was speaking at the start of a two-day UN-backed summit on Friday that has been 10 years in the making and aims to approve a peace framework for the volatile area that includes Rwanda, Burundi and the Democratic Republic of Congo (DRC).
"What is at stake is nothing less than a new era for many millions of African men, women and children, who have been through a lot, who have buried too many relatives, who look to us not to waver in this effort," Annan told at least 13 heads of state gathered in Tanzania's commercial capital.
"We cannot afford to have them write this process off as a theoretical exercise."
Under a pact approved by regional foreign ministers on Thursday and due to be adopted at the Dar es Salaam summit, Great Lakes leaders are expected to pledge greater cross-border cooperation and confidence-building.
Right to intervene
The agreement also calls for moves to disarm rebel groups and build regional security structures, a first step towards ending a violent decade across the region that saw three million people die in war and genocide and from hunger and illness linked to political chaos.
Tanzanian President Benjamin Mkapa, whose country has been among those hit by an influx of refugees, said leaders must now accept their neighbours had a right to intervene in situations such as Rwanda, where 800,000 people died in the 1994 genocide.
"Possibility for intervention must be placed on the table," Mkapa said in his welcoming speech.
The region has seen a decade of
war and genocide
The European Union envoy to the meeting, Dutch Foreign Minister Bernard Bot, vowed rich country support for the peace plan, which he called a "turning point" for the Great Lakes.
"Starting is often the most difficult step. But a start has been made," he said.
The Great Lakes has long been one of Africa's most troubled regions, riven by both ethnic conflict and political rivalries fuelled in part by hunger for its rich natural resources.
Uganda, Rwanda, Burundi and Sudan were already embroiled in civil wars in the early 1990s, but violence escalated after the 1994 genocide in Rwanda, when 800,000 Tutsis and moderate Hutus were slaughtered by extremist Hutus in a 100-day killing spree.
After peace was restored to Rwanda, conflict spread when millions of refugees fled into Burundi and the DRC. Rwanda has invaded the DRC twice, ostensibly to hunt down Hutu rebels who fled after the genocide.
The Dar es Salaam summit comes as transitional governments in Burundi and the DRC struggle with fragile peace deals and to lead their countries to elections in 2005. Uganda and Sudan are trying to end long-running internal conflicts.
Burundi provided an example of the tough road ahead on Thursday as officials in the small central African country postponed a constitutional referendum by one month to December, a further setback in the country's democratisation.
But African officials remained upbeat about prospects for peace and elections both in Burundi and further afield.
Violence escalated after the 1994
genocide in Rwanda
"Delays are to be expected," South African Deputy Foreign Minister Aziz Pahad said. "If countries need more time to get it right, they should be given it."
Among those attending the conference were leaders from Burundi, South Africa, Zimbabwe, the Central African Republic, Republic of Congo, DRC, Kenya, Rwanda, Sudan, Tanzania, Uganda and Zambia.