A short statement would have "noted with concern renewed fighting in some parts of the country" and would have stressed the importance of humanitarian access, according to Reuters, which said it had seen a copy of the draft.
Diplomats said Myanmar neighbor China, with Russia's support, blocked the statement from being issued. China and Russia both have veto power in the council. Diplomats said both countries raised objections, but their UN missions did not reply to requests for comment.
The UN human rights office last month accused the Myanmar military of mass killings and rapes of Rohingya Muslims and the burning of villages. It said its actions "very likely" amounts to crimes against humanity.
About 1.1 million Rohingya live among the country's Buddhist majority. Many among the Buddhist population claim the Rohingya are illegal immigrants from Bangladesh, even though many have lived in the country for decades. The government of former dissident Aung San Suu Kyi has been criticized by international partners for not doing enough to help the Rohingya.
Comment: Suu Kyi told diplomats in the capital, Naypyitaw, that her country was being treated unfairly.
Comment: Russia and China's positions: This is an internal affair to be worked out by Myanmar.