In a statement issued Wednesday, the 15-member council acknowledged the initial attacks on Myanmar security forces but "condemned the subsequent violence," and called for "immediate steps to end the violence in Rakhine, de-escalate the situation, re-establish law and order, ensure the protection of civilians."
According to Matthew Rycroft, the United Kingdom's ambassador to the United Nations, the statement marked the first time in nine years that the Security Council had agreed on this particular issue.
"We were united in our concern about the situation, in the deterioration of the situation and we have heard graphically from the Secretary General and (US diplomat) Jeff Feltman who briefed us on the catastrophe that is befalling Rakhine state and the Rohingya there," said Rycroft.
Earlier on Wednesday, UN Secretary General António Guterres said that the crisis involving the Rohingya Myanmar's Rakhine state had become "catastrophic."
"Grievances that have been left to fester for decades have now escalated beyond Myanmar's borders, destabilizing the region," Guterres told reporters at the United Nations. "The humanitarian situation ... is catastrophic."
More than 370,000 Rohingya have fled to Bangladesh to escape violence since August 25, according to the United Nations, an average of almost 20,000 a day.
Guterres said many women and children were arriving in Bangladesh "hungry and malnourished." Reports of attacks on civilians by Myanmar security forces are "disturbing" and "completely unacceptable," he said.
US Ambassador to the UN Nikki Haley tweeted her gratitude to Bangladesh for taking in the deluge of refugees.
In a statement the government of Bangladesh said it was expanding the camp for the Rohingya refugees and was doing all it could to help, "but it is nearing its limits." Bangladesh "urgently calls on the government of Myanmar to repatriate the Rohigya within Bangladesh's borders, and on the international community to pressure Myanmar to do so."
Bangladesh's appeal was echoed by Guterres. "I call on the Myanmar authorities to suspend military action, end the violence, uphold the rule of law and recognize the right of return of all those who had to leave the country," Guterres said, who also urged countries to provide aid.
The Rohingya Muslims "must be granted nationality or, at least for now, a legal status that allows them to lead a normal life, including freedom of movement and access to labor markets, education and health services," he added.
Suu Kyi has been repeatedly criticized over her response to the crisis.
"One is the current situation in Rakhine state. We have terrorist attacks and also there are many works on public safety and humanitarian works," spokesman Zaw Htay said in a statement.
"And the second reason is we have received reports that there are possibilities of terrorist attacks in our country."
Htay later announced Suu Kyi would give a "state of the union" speech next Tuesday in which she would address the Rohingya crisis fully.
The latest outbreak of violence in Rakhine state was sparked last month by a series of alleged attacks by Rohingya militants on government border posts.
The actions of Myanmar's armed forces are believed to have intensified following the recent attacks, and UN human rights chief Zeid Ra'ad Al Hussein described them Monday as a "textbook example of ethnic cleansing."
Refugees are pouring across the border into Bangladesh, bringing with them stories of murder, rape and devastation.
Some have been injured by landmines they accuse Myanmar of planting along the border, while others described people being tortured to death or burned alive.
The United Nations said the crisis has left at least 1,000 people dead.
CNN's Evan Simko Bednarski and Nima Elbagir contributed to this report.