Muslims in the overwhelmingly Buddhist nation mostly live in poverty in Rakhine state, next to Bangladesh.
In a "historic and highly unusual" move, top diplomats from each of the 15 UNSC member states began a visit to Bangladesh on Saturday and will travel to Myanmar today.
Led by Kuwait, Britain and Peru, the four-day Security Council visit is expected to include a meeting with Bangladesh's Prime Minister Sheikh Hasina, as well as a helicopter flight over Rakhine to allow delegates to see the remains of villages torched during the violence.
Some of the Muslim refugees broke down in tears as they told the ambassadors harrowing stories of murder and rape in Myanmar.
"This is very complicated issue, and it's related with history, with ethnicity, with religions", Chinese deputy UN Ambassador Wu Haitao told reporters, in response to a question about whether China and Russian Federation were preventing the council from considering a resolution on Myanmar.
Russia's ambassador to the UN, Dmitry Polyansky, told reporters that the diplomats would not look away from the crisis, but added that finding a solution would be no easy task.
"This is indeed a very complex issue".
Gaza Protesters Charge Fence; 3 Killed, 100s Wounded
Hamas' Interior Ministry announced that Egypt had agreed to open the Rafah border crossing for three days, beginning Saturday. Gaza Strip was shaken by seven weeks of clashes in the summer of 2014 between Israeli forces and Palestinians.
Extended conversation with Rohingya activist Tun Khin, who visited the world's most densely populated refugee camp in Cox's Bazar, Bangladesh, earlier this month. The Muslim population in Rakhine has either been decimated or fled to Bangladesh.
UN Secretary-General Antonio Guterres' spokesman Stephane Dujarric said the overall population of Rohingya refugees in Bangladesh is now estimated to be over one million. Myanmar authorities claim the military operation in Rakhine is aimed at rooting out extremists and have denied nearly all reports of alleged atrocities committed by its security forces in the region.
The state minister said the UNSC team agreed on broader issues, including the fact that the solution lies in Myanmar as problem is in Myanmar, but there has been no consensus yet on imposing sanction on Myanmar or stronger action against Myanmar.
Hundreds of thousands of refugees are living in temporary shelters made of bamboo and tarpaulins at Kutupalong, many on steep hills and in low-lying areas likely to be flooded. Some carried placards reading "We want justice".
Rohingya population flocked to meet the delegation - five permanent members from China, France, Russia, UK and the U.S., and 10 other non-permanent members - at Kutupalong camp, wielding posters and demanding safe repatriation back to Myanmar.
Ahead of the visit, an global analyst told UNB that Bangladesh needs to provide "strong and unassailable evidence" backed up by documents to make its case before the UN Security Council delegation.
The Security Council, meanwhile, has yet to vote on an official resolution to exert worldwide pressure on Myanmar, although the United Nations and United States - another permanent UNSC member - both branded a brutal military crackdown in Rakhine state that drove almost 700,000 Rohingya to seek shelter in neighboring Bangladesh since last August as "ethnic cleansing".