Bracing for more clashes, thousands of Rohingya, mostly women and children, have decided to try to wade across the Naf River in an attempt to reach Bangladesh.
Around 2,000 people are believed to have made the dangerous journey from Myanmar since Friday, when the latest violence erupted in Rakhine state.
A series of coordinated attacks by Rohingya militants on several police posts signalled a new shift in the long-running conflict.
The militants attacked about 30 police stations and an army base, wielding guns, sticks and homemade bombs.
A smaller attack in October last year was met with brute military force from Myanmar, along with claims of human-rights abuses.
Rohingya refugee Mujibur Rahman says the people just want peace.
“In our village, there was huge fighting. So we have come here, taken shelter near the border, and we want to stay here in Bangladesh, because, in our country, there is much repression, so we are here. We appeal to the Bangladesh government to allow us to stay for some days. After that, when there is peace in our country, we will go back.”
The government of Myanmar says it has evacuated at least 4,000 non-Muslim villagers as fighting continues.
The United Nations has confirmed it has pulled out all non-essential staff from the area.
At least 12 members of the security forces and several civilians are believed to be among the dead.
Advocates for the Rohingya say many people have fled to the mountains or are seeking to cross into Bangladesh.
Witnesses have described seeing several hundred people stuck in a “no man’s land” at one border point, their path blocked by Bangladeshi guards.
The Bangladesh Border Guard’s Lieutenant Colonel Manzurul Hasan Khan says authorities are trying to deal with the situation.
“This morning, we have heard a huge number of fighting on the other side of the border, including explosions. What I think is the reason is, this morning, Rohingya again came down to this side in numbers. They are looking scared. It looks like they are running out of the fear of their life.”
The Rohingya have faced severe restrictions in north-western Myanmar, where they are denied citizenship and their movements are limited.
Many Myanmar Buddhists, who make up the majority of the nation’s population, consider them illegal immigrants from Bangladesh.
But some can trace family connections in Myanmar for generations.
Some analysts are speculating the latest flare-up could be linked to Ata Ullah, the leader of a group that claimed responsibility for last October’s and Friday’s attacks.
Myanmar’s government has declared the group a terrorist organisation and has threatened to take action against it.
The treatment of the more than one million Rohingya living in Myanmar has become a major issue for leader Aung San Suu Kyi, who has faced criticism from the international community.
Speaking in Vatican City, Pope Francis has called for kindness to prevail.
“Sad news has arrived of the persecution of the religious minority, our Rohingya brothers. I’d like to express my full closeness to them. Let us all ask the Lord to save them, and encourage men and women of goodwill to help them, for them to be given their full rights.”
Rohingya have been fleeing Myanmar to Bangladesh since the early 1990s, with around 400,000 now in the country.