UN Secretary-General Antonio Guterres said it is "an absolutely essential priority" to stop all violence against Burma's Rohingya Muslims, allow them to return to their homes, and grant them legal status.
The UN chief said the UN is also insisting on "unhindered humanitarian access" to all areas of northern Rakhine State, where more than 600,000 Rohingyas lived before fleeing to Bangladesh.
Mr Guterres is leaving for Europe and Asia, where he will attend a joint summit between the UN and the Association of Southeast Asian Nations which is certain to address the plight of the Rohingyas.
Burma's de facto leader Aung San Suu Kyi, a Nobel Peace Prize laureate who has faced growing international condemnation over violence against the Rohingyas, is expected to attend the meeting in the Philippines from November 10-14.
Buddhist-majority Burma does not recognise the Rohingya as an ethnic group, insisting they are Bengali migrants from Bangladesh living illegally in the country.
It has denied them citizenship, leaving them stateless.
The latest violence began with a series of attacks August 25 by Rohingya insurgents. Burmese security forces responded with a scorched-earth campaign against Rohingya villages that the UN and human rights groups have criticised as a campaign of ethnic cleansing.
Mr Guterres said: "What has happened is an immense tragedy, and the levels of violence and the atrocities committed are something that we cannot be silent about.
"We insist on the need to make sure not only that all violence against this population stops, but also ... we insist on the need to reassert the right of return."
The secretary-general said the Rohingya must be able to return voluntarily, in safety and dignity, to the areas they came from and not be placed in camps.
Mr Guterres said the root causes of the discrimination that has left the Rohingyas stateless, such as their legal status, must also be addressed.
He has previously urged Burma's government to give the Rohyingyas citizenship, or at least legal recognition, so they can move freely, get jobs and an education, and receive health care.
"We'll go on engaging in all possible domains for these objectives to be finally achieved," the secretary-general said.
Mr Guterres applauded a presidential statement which strongly condemned the violence against the Rohingyas and was approved unanimously by the Security Council on Monday, calling it "an important step forward".
The statement called on Burma's government to "ensure no further excessive use of military force in Rakhine State" and take immediate steps to respect human rights.
It was the strongest council pronouncement on Burma in nearly 10 years, and reflected widespread international concern at the plight of the Rohingyas.