By Agence France-Presse
United Nations, United States,
Annan, who led an advisory commission to the Myanmar government, said world powers must work with the country's military and civilian leaders to end the refugee crisis.
The Security Council is weighing action, possibly a resolution laying out demands, but diplomats have said China, a supporter of Myanmar's former ruling junta, and Russia are opposed to such a measure.
"I hope the resolution that comes out urges the government to really press ahead and create conditions that would allow the refugees to return with dignity and with a sense of security," Annan told reporters after a closed-door meeting with the council.
"They should not be returned to camps. They should help rebuild," he said.
More than 500,000 people, mostly Rohingyas, have since late August crossed into Bangladesh, fleeing military operations in Myanmar's Rakhine state that the United Nations has denounced as ethnic cleansing.
Myanmar authorities say they are rooting out Rohingya militants following attacks on police posts in late August.
The issue of the return of the Rohingyas is shaping up as a major hurdle.
A recent report by the UN human rights office accused Myanmar of seeking to permanently expel the Rohingya, by planting land mines at the border with Bangladesh.
"The international community is now beginning to put pressure on the military," Annan said, adding that "military-to-military talks" were aimed at pressing Myanmar to rein in its operations.
He called on the council to agree with Myanmar on a "roadmap" and warned that without action "we are going to have a long-term festering problem" in the region that "can be very serious, down the line."
In late August, Annan presented the final report of the advisory commission on Rakhine state that he chaired at the request of Myanmar's de facto leader Aung San Suu Kyi.
The report called for granting citizenship and other rights to the Rohingyas, who are stateless and have long faced discrimination in the Buddhist-majority nation.
The UN's top political affairs chief, Jeffrey Feltman, traveled to Myanmar on Friday for talks.