This was announced by the Australian government which said it was "deeply concerned by the escalating violence in Rakhine State in Myanmar and the resulting humanitarian crisis in Myanmar and Bangladesh".
Bangladesh had earlier said the new influx of Rohingya refugees is an unbearable additional burden on the country which has been hosting around 400,000 Myanmar nationals who had to leave their country in the past due to communal violence and repeated military operations.
"The government of Myanmar needs to be told that worldwide support and finance is conditional on a major change in policy towards the Rohingya".
Myanmar's handling of the crisis and perceived persecution of the Rohingya have drawn sharp worldwide criticism, with Bangladesh accusing Myanmar forces of carrying out a "genocide" against the officially stateless Muslim minority group.
The Myanmar military offensive in the western state of Rakhine was triggered by a series of guerrilla attacks on August 25 on security posts and an army camp in which about a dozen people were killed. "We need to see immediate and widespread access to humanitarian aid and relief for the people of Burma (Myanmar) and the people of Rakhine".
In announcing that Suu Kyi would take a pass on the U.N. General Assembly in NY, which opened Tuesday and is expected to run through September 25, a spokesman for Myanmar's presidential office said the decision was made for a number of reasons related to the ongoing situation in the troubled state.
"We urge you to take decisive actions to stop the violence against innocent civilians and bring permanent peace to Rakhine state", they said in the letter.
Ethiopian Ambassador Tekeda Alemu, who is presiding over the council this month, said the 15 member nations expressed concern over the violence that occurred during the Myanmar security forces' counteroffensive.
Rohingya people have faced years of persecution in Myanmar.
Rohingya children, above. Some 16,500 Rohingyas from Myanmar are registered with the United Nations Human Rights Commission (UNHRC) in India.
The Security Council met behind closed doors at the request of Britain and Sweden to try to agree on a response to the crisis, but diplomats said they expected China and Russian Federation to resist calls for a strong statement.
At the request of the United Kingdom and Sweden the UN Security Council also met on Wednesday to discuss the crisis and publicly condemned the situation in Myanmar, formerly known as Burma. He said 270,000 people have fled to Bangladesh to escape the violence.
Bangladesh's Prime Minister Sheikh Hasina has called on Myanmar to take the Rohingya refugees back.
"We are committed to a sustainable solution that will lead to peace, stability and development for all communities within the state", she said then.
Rights groups have called on the Security Council to step up the pressure on Myanmar authorities and make clear the world is watching.