The exodus began Friday after the government intensified "clearance operations"
following an attack by Rohingya militants on border posts, in which 12 security officials were killed.
Myanmar state media reported Tuesday that more than 110 people had died since Friday's "coordinated attacks by extremist terrorists."
While thousands of Rohingya refugees have made it across the border with Bangladesh, thousands of others are stranded in the no man's land between the two countries, said an IOM spokesperson.
IOM said it's unclear how many people have made it into camps along the Bangladeshi border. Numbers are being compiled by aid agencies working in the camps as there is no registration process for Undocumented Myanmar Nationals (UMNs) in Bangladesh.
Report: 'Status quo cannot continue'
The violence erupted hours after a long-awaited report into the treatment of Rohingya by the Advisory Commission on Rakhine State, led by former United Nations Secretary-General Kofi Annan.
The report warned that unrest in Rakhine could spiral out of control unless concrete action is taken soon.
"Tensions remain high and they risk becoming worse," Annan said. "The status quo cannot continue."
The Rohingya, a Muslim minority in the predominantly Buddhist Myanmar, are considered some of the most persecuted people in the world. Myanmar, also known as Burma, considers them Bangladeshi interlopers and Bangladesh says they're Burmese.
Refugees at the border told CNN Monday that Myanmar army soldiers had shot at them with mortars and machine guns.
"We want to go and take shelter inside Bangladesh and don't want to go back with my innocent children in the lion's mouth again," Amena Khatun, a Rohingya woman, said. "I don't see any light of hope."
United Nations meeting
The UN Security Council held a closed door discussion Wednesday at the request of the United Kingdom to address the escalating violence in Myanmar.
British Ambassador to the UN Matthew Rycroft told reporters resistance from some countries meant there was unlikely to be consensus on any action from the UN. No joint statement was released.
"What we want to do is shine a spotlight given the reports of provocative military acts and increasing refugee flows. I think it's important that all of the parties de-escalate now to reduce tensions and look to the long-term," Rycroft said.
Asked whether the Security Council had a message for the country's leader Aung San Suu Kyi, Rycroft said: "The message is that she has a huge amount of support around that table. A lot of us are hugely supportive allies of hers who have followed her progress with admiration from afar and we look to her to set the right tone and to find the compromises and de-escalation necessary in order to resolve the conflict for the good of people in Burma."
However, rights groups in the region are critical of the role that Suu Kyi, whose National League for Democracy party swept to power in 2015. While constitutional rules prohibit her from holding the office of President, as State Counsellor she acts as the country's de facto leader.
Earlier this week, Matthew Smith, a founder and Chief Executive Officer of human rights group Fortify Rights told CNN that the country's leader is being "irresponsible" with her comments on the situation in Rakhine.
"Aung San Suu Kyi has been putting out statements (which are) consistently disturbing, and her office is generating anti Rohingya, anti-aid worker propaganda, fueling tensions in the country.
"As de facto head of state Aung San Suu Kyi needs to be calling for calm, calling for military to use restraint. SK's messaging could not be more irresponsible right now."
Smith said the stories being told by Rohingya refugees who have fled their homes are consistent with his previous understanding of the military's treatment of civilians.
"Based on the (Myanmar) army's consistent response in the last couple of months, we know that they have committed mass killings, mass gang rape, (and) razed (Rohingya) villages. Reports of them opening fire on civilians is certainly plausible," he said.
After similar violence broke out in October 2016, approximately 85,000 civilians fled to Bangladesh, the ministry said.
Secretary of the Ministry of Foreign Affairs Mahbub Uz Zaman expressed "serious concern at the possibility of recurrence of such a situation" and urged Myanmar to protect its civilian population, according to a Ministry statement.