* China calls for ceasefire in Myanmar's Rakhine State
* Offers to keep playing a constructive role on the issue
* Key is to prevent rekindling of flames of war, it says
* Diplomats from 51 nations gather for talks (Adds comment by China's Wang to Myanmar president; paragraph 8)
By Yimou Lee
NAYPYITAW, Nov 20 (Reuters) - China called for a ceasefire in Myanmar's Rakhine State so that Rohingya Muslim refugees can return from Bangladesh, proposing a three-stage approach to the crisis as diplomats from 51 mostly Asian and European countries gathered in Myanmar on Monday.
More than 600,000 Muslim Rohingya have fled to Bangladesh since late August, driven out by a military clearance operation in Buddhist majority Myanmar's Rakhine State.
Amid a burgeoning humanitarian catastrophe, rights groups have accused the Myanmar military of atrocities, while foreign critics have blasted Aung San Suu Kyi, the Nobel peace prize winner who leads a civilian administration that is less than two years old, for failing to speak out more strongly.
On Monday, Suu Kyi opened an Asia-Europe Meeting for foreign ministers that had been scheduled in Myanmar before the outbreak of the crisis.
Speaking in the capital of Naypyitaw on Sunday, having arrived from Dhaka, China's Foreign Minister Wang Yi said China believed Myanmar and Bangladesh could work out a mutually acceptable way to end the crisis.
"The first phase is to effect a ceasefire on the ground, to return to stability and order, so the people can enjoy peace and no longer be forced to flee," China's foreign ministry said in a statement, citing Wang.
"With the hard work of all sides, at present, the first phase's aim has already basically been achieved, and the key is to prevent a flare-up, especially that there is no rekindling the flames of war."
During a meeting on Sunday, the ministry said, Wang told Myanmar President Htin Kyaw, "As a friend of both Myanmar and Bangladesh, China is willing to keep playing a constructive role for the appropriate handling of the Rakhine State issue."
Visiting Myanmar last week, U.S. Secretary of State Rex Tillerson made many of the same points, but he also called for a credible investigation into reports of atrocities.
Once a ceasefire is seen to be working, Wang said talks between Myanmar and Bangladesh should find a workable solution for the return of refugees, and the final phase should be to work toward a long-term solution based on poverty alleviation.
Myanmar and Bangladesh officials began talks last month to settle a repatriation process for Rohingya refugees, which Bangladesh expects to take to the next level in coming days.
Speaking on the sidelines of the ASEM meeting, European Union foreign policy chief Federica Mogherini said, "We believe that stopping the violence, the flow of refugees and guaranteeing full humanitarian access to Rakhine state, and safe, sustainable repatriation of refugees are going to be key."
Mogherini, who also visited Bangladesh over the weekend, said, "There's a real possibility of Myanmar and Bangladesh reaching a memorandum of understanding and agreement for the safe repatriation of refugees to Myanmar."
The European bloc was ready to help with the process, she added.
It was unclear, however, whether a safe return was possible, or advisable, for the thousands of Rohingya women and children still stranded on the beaches trying to flee hunger and instability in Rakhine.
Myanmar intends to resettle most refugees who return in new "model villages", rather than on the land they previously occupied, an approach the United Nations has criticized in the past as effectively creating permanent camps.
Besides restoring peace for Rohingya to return, Myanmar also had to resolve the issue of their citizenship, having treated them as stateless for decades, the U.N. High Commissioner for Refugees, Filippo Grandi, told a news conference in Tokyo.
The UNHCR was ready to assist both countries with repatriation, he said, adding that it could help Myanmar with the citizenship verification of the Rohingya. Until now it has not been invited to participate in either.
"Much as resources are needed in Bangladesh to respond to the crisis, the solutions to this crisis lie in Myanmar," Grandi said.
VIOLENCE LARGELY OVER
The crisis erupted after the military launched a brutal counter-insurgency operation against the militants after attacks on an army base and 30 police posts in Rakhine on Aug. 25.
Myanmar's military has said that all fighting against the Rohingya militants died out on Sept.5.
The group behind those attacks, Arakan Rohingya Salvation Army (ARSA), had declared a one-month ceasefire on Sept.10, which was rejected by the Myanmar government. But there have been no serious clashes since.
The United States and other Western countries have become more engaged with Myanmar since it began a transition to civilian government after nearly 50 years of military rule.
Myanmar's generals retain autonomy over defence, internal security and border issues in the current power-sharing arrangement.
China, with close ties to both Myanmar and Bangladesh, has long been a key player in lawless borderlands where rebel ethnic groups have battled Myanmar's government for decades in a conflict driving thousands of refugees to seek shelter in China. (Reporting by Ben Blanchard in BEIJING, Antoni Slodkowski in YANGON and Thomas Wilson in TOKYO; Editing by Simon Cameron-Moore)