In a unanimous statement, the 15-membered powerful wing of the UN also demanded safe, unhindered access for its agencies and their partners to provide humanitarian assistance.
Britain and France dropped a push for the Security Council to adopt a resolution on the situation to appease council veto power China, a supporter of Myanmar's former ruling junta.
The Council instead unanimously agreed on a formal statement. It is only for the third time in nearly a decade that the UN Security Council adopted a presidential statement on Myanmar.
The unrest in troubled Rakhine state began after deadly attacks on police stations across the state, blamed on a newly emerged militant group, the Arakan Rohingya Salvation Army (Arsa).
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Scores of people were killed in the ensuing military crackdown, and there are widespread allegations of villages being burned and Rohingya being driven out.
The military in Myanmar says its operations are aimed at rooting out militants, and has repeatedly denied targeting civilians. Survivors, witnesses and refugees have contested this.
Through the statement read out by its President for the month of November, Sebastiano Cardi from Italy, the Council urged Myanmar to support the voluntary, safe and dignified return of displaced people and refugees to their homes in Rakhine State.
It commended the efforts undertaken by Bangladesh, with the assistance of the United Nations, their partners and other nongovernmental organisations, to provide safety, shelter, and humanitarian assistance to those who have fled the violence.
Britain has repeatedly called on the Myanmar security forces to protect all civilians and act now to stop the violence and allow humanitarian aid to urgently reach all those who need it, he said.
"We are encouraged to see State Counsellor Aung San Suu Kyi making important steps forward, including establishing a domestic body to deliver humanitarian and development assistance in Rakhine although this cannot substitute for UN agencies and making efforts to promote interfaith and inter-communal harmony, including a recent visit to northern Rakhine," he added.