According to Mr Zaw, Ms Suu Kyi is needed in Myanmar to "manage humanitarian assistance" and "security concerns" caused by the violence, as competing rumours ratchet up anti-Muslim rhetoric across the Buddhist-majority country.
Guterres said the situation in Myanmar's western state of Rakhine can be described as ethnic cleansing.
The latest wave of Rohingya fleeing their homes began on 25 August, following attacks by Rohingya militants on police and military posts. "It's about the Security Council uniting and sending a very public message to the government of Myanmar that they have to put an end to the ongoing violence". They have been denied citizenship rights and are viewed by the local authorities as illegal immigrants from Bangladesh.
Human rights groups have urged the UNSC to increase pressure on Myanmar's authorities regarding the plight of the Rohingya and make clear the world is watching.
Bangladesh is struggling to provide relief for exhausted and hungry refugees - some 60 per cent of whom are children - while almost 30,000 ethnic Rakhine Buddhists as well as Hindus have also been displaced inside Myanmar.
According to different organizations, recent military offensives by the Myanmar Army in Rakhine State has led to the killing of hundreds of Rohingya people. "We need to see immediate and widespread access to humanitarian aid and relief for the people of Burma (Myanmar) and the people of Rakhine".
Myanmar's leader Aung San Suu Kyi has been widely condemned for a lack of moral leadership and compassion in the face of the crisis, denting the Nobel peace laureate's reputation.
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"As NPR's Colin Dwyer writes, the stream of refugees crossing the border into Bangladesh have brought with them "[reports] of unbridled murder and arson, rape and persecution. sketching a stark portrait of government violence".
But China blocked a proposal from Egypt to add language on ensuring the right of return to the Rohingya sheltering in Bangladesh, diplomats said.
Tekeda Alemu, Ethiopia's ambassador to the United Nations and president of the Security Council for September, suggested after reading the remarks that he wished the council had gone "a little bit further" in its response, but said that as president of the council he could not make any further comments about the strength of the statement.
The Secretary-General also said he has spoken to Suu Kyi several times.
In a statement issued in Lucknow on Wednesday, Mayawati said that the Centre should not force state governments to adopt a stern stand towards Rohingya refugees.
"We have heard them saying, 'No Rohingya in Myanmar.' But we will go back", Arif said.
Global aid groups such as the Red Cross have been confronting the hard task of tending to those crossing the border from Myanmar, averaging 20,000 a day.