Police fired tear gas to scatter protesters in Bangladesh on Thursday, while authorities cut some mobile internet services as violent clashes that have killed six and injured hundreds this week showed no signs of slowing.

Shops and offices were open in Dhaka, the capital, but there were fewer buses on the streets, as a call for a nationwide shutdown from students demanding abolition of a quota of 30% reservations drew little response.

Police fired tear gas to disperse stone-throwing students who blocked a major highway in the southern port city of Chittagong as mobile services were halted across most of the South Asian country.

"Mobile internet has been temporarily suspended due to various rumours and the unstable situation created ... on social media," Zunaid Ahmed Palak, the junior information technology minister, told reporters.

Services would be restored once the situation returned to normal, he added.

The protests are the first significant challenge to Prime Minister Sheikh Hasina's government since she won a fourth straight term in January in an election boycotted by the opposition Bangladesh Nationalist Party (BNP).

Angered by high youth unemployment, with nearly 32 million out of work or education among a population of 170 million, the students are pushing for abolition of the quota of 30% reservations for the families of freedom fighters.

Sporadic clashes were reported in several places as demonstrators blocked major highways, while witnesses said riot police fought pitched battles with protesters in several places in Dhaka.

Authorities had shut all public and private universities indefinitely from Wednesday and sent riot police and the Border Guard paramilitary force to university campuses to keep order.

In a speech on Wednesday, Hasina promised her government would set up a judicial panel to investigate the deaths after police fired bullets and tear gas to scatter protesters.

On August 7, the Supreme Court will hear the government's appeal against a High Court verdict that ordered reinstatement of the 30% reservation for the families of those who fought in the 1971 war of independence from Pakistan, she added.

Hasina asked the students to be patient until the verdict.

The violence was sparked by nationwide clashes between thousands of protesters and members of the student wing of Hasina's ruling party, the Awami League. At least three students were among the six killed in Tuesday's clashes, police said.

The demonstrations intensified after Hasina, the daughter of Sheikh Mujibur Rahman, who led Bangladesh to independence, refused the protesters' demands.

Rights groups, such as Amnesty International, as well as the United Nations and the United States, have urged Bangladesh to protect peaceful protesters from violence.