It's unclear how many refugees have crossed the border, but community leaders in different camps in Bangladesh said at least 3,500 new refugees have entered the country in the last five days.
The alleged insurgents carried out a series of coordinated attacks against police outposts and an army base Friday. It followed a renewed wave of government security operations in the region.
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.
Crossing the Naf river to safety
Sayra Begum, a 28-year-old Rohingya woman from Tomru village in Rakhine, spoke to CNN from an overcrowded, under-supplied refugee camp on the border.
She said her husband and brothers had taken a group of 26 people, including children, to the Naf river which separates Bangladesh and Myanmar. The men stayed in Rakhine, while the others crossed the river to safety.
"We waited till nightfall and later entered in Bangladesh, escaping the eyes of Bangladeshi border guards. We arrived at the (Balukhali refugee camp) but don't know where will we stay and what we will eat."
The camp was set up in October last year when an earlier influx of as many as 85,000 Rohingya crossed the border. It's the closest refugee camp to Myanmar and a common staging post for those who have fled.
One refugee, Amena Khatun, 31, told CNN that the Myanmar army had shot at her and her companions as they made their escape Sunday.
Initially, troops, along with Buddhist civilians "went mad after they found three Buddhists' bodies near a Rohingya village," she said.
"They then came in midnight and started setting fire to our straw made huts. We ran to the hills for our lives."
Khatun said the soldiers shot at them with mortars and machine guns from their border posts, but she and her family clambered over barbed wire fences to enter the no man's land in between the two countries.
"Bangladesh border guards didn't let us in. Since then we are sitting in this marshy land with my entire family," she said tearfully, speaking through the fence that divides her from relative sanctuary.
"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. I don't see any light of hope."
Khatun, along with her family, were eventually allowed to cross the border and enter the camp.
Border Guards Bangladesh (BGB) commanding officer Mozural Hassan Khan told media that he and his soldiers had heard a "huge number" of shots and explosions on the Myanmar side of the border.
"They crossed their fences inside Myanmar border and they came near to the zero line (the border between the two nations). Right now all of them are waiting at zero line. They are looking scared, looks like they are running out of the fear for their life."
Pattern of behavior
Matthew Smith, a founder and Chief Executive Officer of human rights group Fortify Rights told CNN from Bangkok the reports 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."
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, warned Friday that unrest in the state 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."
Myanmar's de facto leader, Aung San Suu Kyi
has been criticized for her government's response to the crisis. "Aung San Suu Kyi has been putting out consistently disturbing statements," Smith says.
"Her office is generating anti-Rohingya, anti-aid worker propaganda (and) fueling tensions in the country. As the de facto head of state Aung San Suu Kyi needs to be calling for calm, calling for military to use restraint.
"(Her) messaging could not be more irresponsible right now."
Pope: Give Rohingya 'full rights'
The Vatican on Monday confirmed Monday Pope Francis will travel to the region later in the year -- he'll visit Myanmar from November 27 to 30, and Bangladesh from November 30 to December 2.
During Sunday prayers, the pontiff expressed solidarity with Myanmar's persecuted Rohingya Muslim community, calling for them to have "full rights."
"We received sad news of the persecutions of the religious minority, our brother Rohingya," he said.
"I want to express all my closeness to them and we ask the Lord to save them and (we ask) for the help of all men and women of good will to give them full rights. We pray for the Rohingya brothers."
The weekend's flashpoints could be the beginning of another mass exodus of Rohingya, a group which rights groups say have been persecuted by Myanmar authorities for decades.
"We're only a few days into" the latest crisis, Smith said, saying that he expected tens of thousands to flood across the border in the coming days and weeks.
The existing camps on the Bangladesh border, already full of Rohingya refugees who are languishing in poor conditions and stuck in legal limbo, are subject to immediate, further overcrowding, Smith says.
According to the Rohingya residents of the Balukhali camp, Bangladesh law enforcers have threatened them not to provide shelter to any newcomers or else they would be "evicted, fined and deported".
A community leader in the camp, seeking anonymity, said: "We are refugees ourselves. Despite broken hearts for our fellow Rohingya, we cannot let them stay here or else we might be driven back to (the) border."
The UNHCR has seen at least 3,000 new arrivals to their official camps in the last 72 hours, UNHCR Bangladesh's Joseph Surjamoni said.
Amongst the intake are mostly women and children, he said, including a significant number of unaccompanied minors. He added that the nature of the movement of people is "fluid at the moment."
He added that people from the community are there, "extending aid" to the refugees.
The "humanitarian needs on the Bangladesh side are great," says Fortify Rights' Smith.
Bangladeshi border guards are turning people away in an attempt to discourage refugees from seeking safe havens in Bangladesh, he said, but many people are waiting near the border before attempting another crossing.
However, "the Bangladeshi authorities need to provide protection -- they have a legal obligation not to send people back," he said.
In a statement Friday, Bangladesh's 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.