Mujibur Rahaman, 48, who has fled along with five family members from Dekibunia area of Maungdaw in Rakhine, said, "Myanmar army and Myanmar Border Guard Police (BGP) have been torching our houses and showering bullets".
The villagers were caught roughly four kilometers inside Bangladeshi territory en route to a refugee camp in Kutupalong, where thousands of Rohingyas already live in squalid conditions, according to local police chief Abul Khaer.
On Saturday, the government directed the local administration to employ its best efforts to restrict the entry of fresh Rohingyas into the country saying not a single person will be allowed in the name of "humanity".
In its latest report on Sunday, the office of State Counsellor Aung San Suu Kyi, said the death toll from the clashes between security forces and Rohingya rebels that started on Thursday has reached 96 - mostly alleged Rohingya attackers but also 12 security personnel.
"Around 2,000 to 2,500 Rohingyas got into Bangladesh from Myanmar this evening [yesterday]", chairman of Ghumdum Union Parishad Md Zahangir Alam said.
According to the United Nations High Commissioner for Refugees (UNHCR), over the past years Myanmar military forces allegedly in connivance with extremist Buddhist groups have launched major crackdowns on Rohingya Muslims, driving over 74,000 refugees to seek shelter in Bangladesh by February this year.
Tens of thousands of Rohingya Muslims fled their homes after violence killed more than 90 people in Myanmar's Rakhine State.
While the chaos and lack of access made detailed assessments hard, experts said the latest attacks were so widespread, they appeared to be more akin to a movement or an uprising, rather than an insurgent offensive.
Pope Francis recites the Angelus noon prayer from the window of his studio overlooking St.Peter's Square, at the Vatican, Sunday, Aug. 27, 2017.
This photo, taken on December 25, 2016, shows Rohingya Muslims from Myanmar who tried to cross the Naf River into Bangladesh.
The military, known as the Tatmadaw, reported several clashes involving hundreds of Rohingya insurgents across northern Rakhine state on Sunday.
Just since previous year, around 87,000 Rohingya have fled to Bangladesh amid a military crackdown on insurgents in Myanmar's western Rakhine state, giving way to horrifying stories of rapes, killings and arson by security forces.
"We wish to return to Myanmar if the government provides us nationality and citizenship", said Shafiul Mostafa, another registered Rohingya refugee at Cox's Bazar.
The treatment of approximately 1.1 million Muslim Rohingya in mainly Buddhist Myanmar has emerged as the biggest challenge for national leader.
The majority of Rohingya have been in Myanmar for multiple generations.
The army denies the allegations which included civilian killings and mass rape. They do not find mention in that country's official listing of 135 ethnic communities, and are thus not recognised as citizens by Myanmar.