Annan, who led the Myanmar government-formed ‘Advisory Commission on Rakhine State’ to probe the crisis, emphasised changing the law to grant citizenship to the Muslim minority population.
Annan was speaking at a meeting organised by the UK and France at the UN headquarters in New York on Friday. Representatives to the UN from Bangladesh and Myanmar also addressed the meeting.
Over half a million Rohingyas have fled the border state of Rakhine since a military crackdown began on Aug 25.
About 400,000 other Rohingya refugees have been living in Bangladesh for the past few decades after fleeing persecution in neighbouring Myanmar.
The commission had recommended granting citizenship to Rohingyas and the repatriation of Rohingya refugees in Bangladesh.
The UN is weighing action on the issue.
"I hope the resolution that comes out urges the Myanmar 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 Annan said he was hopeful the Myanmar government would adopt the recommendations of his commission and bring stability to Rakhine.
"The international community is now beginning to put pressure on the military," he said.
Without action "we are going to have a long-term festering problem" in the region that "can be very serious, down the line," warned the former UN secretary-general.
She has also promised to take back 'verified refugees' who have fled to Bangladesh.
Both countries would benefit from bilateral cooperation and border security, said Annan.
Bangladesh Permanent Representative to the UN Masud Bin Momen repeated Prime Minister Sheikh Hasina’s comments at the UN General Assembly that the solution to the crisis lays in Myanmar.
Bangladesh has been patient despite Myanmar’s violation of its airspace and provocations, he said.
Momen added there was a significant difference between the Myanmar government’s remarks on the issue and the situation on the ground.
The UN Security Council has discussed the Rohingya issue three times between Aug 28 and Sept 13. On Sept 13, it expressed its concern regarding the situation in Rakhine state.
Permanent members Russia and China have sided with Myanmar on the issue, while the UK and France have opposed it. The US has condemned the violence in Rakhine.