Annan, whose commission recently compiled a report on the refugee crisis, told an informal Security Council meeting Friday that Myanmar's government must "create conditions that allow the refugees to return with dignity."
Refugees sheltering in neighboring Bangladesh needed assistance to "get their homes back" and should not be returned to camps, Annan insisted.
Over the last weeks, more than 500,000 people, mostly Rohingyas, have fled Myanmar's Rakhine state into Bangladesh, escaping what the UN's Human Rights Office said were "systematic” attacks by Myanmar security forces.
Myanmar authorities, however, said they were rooting out Rohinga militants following attacks on 30 police posts on August 25 and denied UN allegations of ethnic cleansing.
Safe conditions needed
Annan urged the Security Council Friday to agree with Myanmar on a "roadmap” and warned that if safe conditions for returns were not created the world community would be stuck with a very serious, long term "festering" problem.
Myanmar's military on Friday said it had launched an internal probe into troop responses to August's insurgency by the Rohingya militia, but insisted the sweep had been justified under Myanmar's Buddhist-majority constitution.
Civilian leader Aung San Suu Kyi said Thursday that she had formed a committee to oversee international and local assistance in Rakhine.
Previous internal probes have largely dismissed refugees' claims of abuses.
Army chief Min Aung Hlaing claimed via Myanmar state media on Friday that photos showed Muslims "departing calmly rather than fleeing terror."
Co-chairing Friday's Security Council meeting, French ambassador Francois Delattre said the briefing with Annan should have helped to overturn "the totally unacceptable status quo."
The Chinese and Russian UN missions did not comment on the diplomatic initiative.
Myanmar's Buddhist majority typically regards the Asian nation's roughly one million Rohingya as having migrated illegally from Bangladesh, although many have lived in Myanmar for generations.
Rohingya were stripped of their citizenship in 1982. About 120,000 live in camps outside Rakhine's capital, Sittwe, following earlier waves of displacement.
ipj/jm (Reuters, APF, AP, dpa)