Bangladesh police on Tuesday said they shot dead two members of the country's Jamaat-i-Islami party in gunfights, as a rights activist demanded an independent probe on concerns of extrajudicial killings.

Security forces have launched a major crackdown on suspected militants since a Dhaka cafe was attacked in July and left 22 mainly foreign hostages dead.

But the crackdown which has seen a string of suspects killed in gun battles has sparked concerns that opposition activists were among those being targeted.

"Jamaat-e-Islami party leader from the western district of Jhenaidah and a leader of its student wing were killed early on Tuesday," said Senior police officer Azbahar Ali Sheikh.

“They fired from pistols and threw three (molotov) cocktails at policemen when they challenged them at 3:45 am. We fired back and two people were hit and we learnt their identities later,” the officer told AFP.

Top human rights activist Nur Khan Liton has demanded a judicial probe into the killings.

“We've serious questions about these deaths. We think these are extrajudicial killings,” Liton told AFP, saying local newspapers had earlier reported the party workers missing.

A senior Jamaat official denied the two party figures were killed in gunfights, saying both had been picked up by plain-clothed policemen early last month.

“It is cooked up (by police),” he told AFP on condition of anonymity.

The Bangladesh government had launched a nationwide crackdown on Jamaat activists in recent years, following deadly protests in which tens of thousands of Islamists were either detained or charged.

Bangladesh charges BNP official with Italian's murder

A Bangladesh court on Tuesday charged an opposition party leader with the murder of an Italian aid worker, drawing an angry reaction from the party which accused the government of trying to discredit it.

M.A Quayum, the Dhaka city leader of the main opposition Bangladesh Nationalist Party (BNP), was indicted in absentia over the killing last year of the Italian charity worker Cesare Tavella.

Dhaka police have said the murder was part of a conspiracy to smear the secular government and destabilise Bangladesh, which has suffered a series of Islamist attacks on foreigners and religious minorities.

“The court will start hearing the witnesses from November 24. Five people are now in custody. Quayum and another (indicted person) are still absconding,” prosecutor Abdullah Abu told AFP.

Tavella was shot dead in Dhaka's diplomatic zone in September last year by assailants riding on a motorbike.

Bangladesh's elite security force Rapid Action Battalion (RAB) said last week he was killed by a new faction of the Jamayetul Mujahideen Bangladesh (JMB), an extremist group.

But the militant Islamic State group had also claimed responsibility.

The BNP said charging Quayum, who is believed to be living in exile in Malaysia, reflected “the government's malicious intent”.

“The RAB DG said the new-JMB is responsible for Tavella's murder. But today we saw that Quayum was indicted over the murder,” senior BNP official Asaduzzaman Ripon said.

“Which one shall we believe as the truth? The government is trying to taint BNP's image internationally by blaming our party men for an incident that we condemned in the first place,” Ripon told AFP.

Human rights activist Nur Khan Liton said demanded a fresh investigation.

“Different law enforcing agencies are presenting different versions (of information about the murder),” he told AFP.

“Therefore, it shows the weakness in the charge sheet. We demand re-investigation to find out the truth," he added.

Bangladesh has also reeling from a wave of recent attacks by militants, with targets including foreigners, rights activists and members of religious minorities.

But the attack on the upmarket Dhaka cafe in July was by far the deadliest. IS group claimed responsibility, but Bangladesh's government has staunchly denied that IS has gained a foothold in the country and instead blamed a local extremist outfit.

Security officials said last week that the head of the militant Islamist group blamed for the cafe siege had died while trying to evade arrest.