The number of displaced is expected to rise, and possibly double, in the coming days.
More than 400 people have been killed in the clashes, some of the worst fighting in decades in a state prone to religious and ethnic conflict. Burma's government says 371 of the dead are Rohingya fighters, 15 are from the security forces and civil service, and 22 are civilians.
Much is in dispute in Rakhine state, where an estimated 1.1 million Rohingya Muslims live in uneasy relations with their Buddhist neighbors.
Rohingya activists and monitors say many of the dead are noncombatants and that massacres — including decapitations — have taken place. They also argue the death toll is much higher.
The government says Rohingya militants and supporters are burning their own homes, spreading fake news, and killing their own people, including informants.
"It is the terrorists who are cutting off heads, and this needs to be known by you and the rest of the world," Burma's national security adviser, Thaung Tun, said Wednesday at a news conference.
What is not in dispute is the epic migration unfolding.
"I've worked in many war zones. I've worked with refugees before. But the scale of this particular flow of refugees is highly distressing," said Tejshree Thapa, senior South Asia researcher at Human Rights Watch.
Thapa witnessed the exodus in Cox's Bazar in Bangladesh on the border with Burma.
"I've spoken to people who have walked four or five days through mountains, across rivers," she said. "It's wave after wave. I mean, you stand at the border and it's just family after family. It's endless. You drive down one patch of road, you see thousands of people. You turn down another patch of road and see thousands."
The story of the Rohingya, the world's largest stateless group, is a story of movement.
In the decades after World War II, tens of thousands fled an increasingly unwelcoming Burma, with waves occurring in the 1970s, 1980s and 1990s.
There are Rohingya diaspora communities in Malaysia, India, Nepal, Saudi Arabia and Pakistan. But the biggest is in Bangladesh, where hundreds of thousands of Rohingya live, many undocumented.
In 2012, intercommunal violence in Rakhine state sent more than 140,000 Rohingya into internal displacement camps, where many remain today. In 2014, tens of thousands fled the country by sea.
Last year, nearly 90,000 escaped to Bangladesh after ARSA first emerged with deadly assaults on border guard posts, triggering a crackdown by the military that has resulted in allegations of possible crimes against humanity.
Organized armed resistance is nothing new, but it has taken different forms and names over the years. ARSA was formed in the aftermath of the violence in 2012, with ties to the diaspora.
Burma's government insists on calling the Rohingya "Bengali," implying that they are illegal immigrants.
The length of the trip from Burma to Bangladesh can depend on a variety of factors, not least geography.
Those closer to Maungdaw, a town near the top of northern Rakhine, are positioned closer to the Naf River separating the two countries and may be able to cross that way.
But at least 57 people have died after their boats capsized trying to make the trip.
Those living further south have to navigate security patrols, some of which have reportedly involved civilians. Making the trip on foot further north involves a longer, hilly journey that can take almost two weeks.
There are other problems. The monitoring group Fortify Rights, for example, has documented instances of ARSA fighters preventing men from fleeing.
Health officials and rights monitors in Bangladesh say hospitals are filled with patients needing serious medical care. There are food, water and medical scarcities, and hospitals are overwhelmed.
Some arrive long after getting hurt.
"The patients came here many days after they received bullet injuries inside Myanmar," Sumon Barua, the chief of a medical facility in Teknaf, near the border, said, using another name for the country.
Rakhine state has been declared a military operations zone, and government officials have implied that ARSA members could be mixing in with civilians to elude capture.
But many Rohingya describe fleeing an aggressive army campaign that does not distinguish between militants and civilians.
Mohamed Ayat, 22, said he was shot twice in the leg on Friday when he tried to flee his house after the army tried to burn it down.
"I couldn't leave my house before September 1 as there was heavy firing [in the area]," he said.
He left without any food.
A man who identified himself only as Arafat said he fled along with six family members, including his wife, son, sister and two nephews.
He says the Burmese military set fire to their homes in northern Rakhine on Aug. 31, forcing them to leave the area and that a member of the security forces killed his 14-year-old cousin.
They walked for two days to reach the border and then crossed on a tiny boat on Saturday, he said.
Stories of experiences inside northern Rakhine, which is largely closed off to the media, could not be independently verified.
Videos circulating online depict groups of refugees massed in a no man's land along the border, and one appeared to show a trail of people gingerly stepping over a small strip of tarp that had been placed over barbed wire.
Burma's de facto leader, Aung San Suu Kyi, whose new administration is less than two years old, has come under increased pressure for not doing more to speak up for the Rohingya.
Though she rarely weighs in on developments in Rakhine, she told Turkish President Recep Tayyip Erdogan on Tuesday that the government is defending all the people of the state, according to a readout of the call.
ARSA on Wednesday called on the international community to put "maximum pressure" on the Burmese government to stop committing what it called "war crime, genocide, and crimes against humanity."
Muktadir Rashid contributed to this report from Dhaka.