It is the first time the council has taken any action over Myanmar and marks a shift of position by China, which had previously used its veto to stop the 15-nation body from voicing criticism of Myanmar's military government.
The statement called on Myanmar and all other parties concerned to work together towards a de-escalation of the situation and a peaceful solution.
It also said the Myanmar government should "create the necessary conditions for a genuine dialogue with Daw Aung San Suu Kyi [the democracy leader] and all concerned parties and ethnic groups in order to achieve an inclusive national reconciliation".
Meanwhile, the UN said Ibrahim Gambari, its special envoy to Myanmar, would set off over the weekend for a tour of Asia.
"Where are the peace and human rights defenders of the world (the super powers)? They haven't done enough in this case. Isn't there oil in Myanmar?"
Lost Soldier, Arusha, Tanzania
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The trip is expected to culminate in what would be the envoy's second visit to Myanmar since the demonstrations erupted.
Ban Ki-moon, the UN secretary-general, is to send Gambari first to Thailand, where he will hold talks on Monday.
A UN statement said that this would be followed with visits to Malaysia, Indonesia, India, China and Japan "with a view to returning to Myanmar shortly thereafter".
Gambari, who returned from a four-day visit to Myanmar last week, had originally planned to make a second visit in the middle of November.
UN diplomats said they hoped that Gambari, who aims to secure the release of political detainees and get a political dialogue started, would be in Myanmar before the end of October.