Four Bangladeshi fishermen were injured when Myanmar's navy allegedly opened fire on them while they were fishing along the countries' troubled border in the Bay of Bengal, an official said Wednesday.

A group of 14 fishermen, four of whom have been hospitalised with bullet wounds, told coastguard officials that a Myanmar navy ship had entered Bangladeshi waters and opened fire on their trawler on Tuesday.

"They said the navy ship started firing on them without any warning," coastguard officer Saiful Absar told AFP by phone from southern Saint Martin's Island, which is close to where the alleged incident happened.

"Four fishermen were injured. They had bullet wounds all over their hands and feet," he said, adding they had been taken to a hospital in the coastal district of Cox's Bazar.

The coast guard is investigating whether the Myanmar Navy had intruded into Bangladesh's territorial waters, he added.

The incident comes as tensions along Bangladesh's southeastern border with Myanmar's Rakhine state run high, after Myanmar's military launched a massive crackdown on Rohingya Muslims in October.

Myanmar's army says it is hunting militants behind deadly raids on police posts.

But Rohingya survivors have described rape, murder and arson at the hands of soldiers -- accounts that have raised global alarm and galvanised protests around Southeast Asia.

More than 34,000 Rohingya have since fled to Bangladesh, which has deployed extra border guards to prevent a large-scale influx of refugees.

Thousands of the fleeing refugees have been sent back to Myanmar by Bangladeshi border guards.

More than 230,000 Rohingya already live in Bangladesh, most of them illegally, although around 32,000 are formally registered as refugees.

But Dhaka is wary of accepting more Rohingya fearing it would encourage the Buddhist-majority country to push more of the stateless minority into densely populated Bangladesh, amid growing local resentment over the new arrivals.

Amnesty International has said Myanmar's military has committed atrocities against the minority group which are tantamount to "crimes against humanity", while Human Rights Watch published satellite images showing hundreds of burned down houses in Rohingya villages.