A Bangladeshi paramilitary unit that receives training from British police has resumed killing people in so-called "crossfire" incidents that human rights groups say are extrajudicial killings.

The Rapid Action Battalion (RAB) – condemned by human rights group as a "death squad" – ceased the killings briefly after the existence of the British training programme was disclosed in US diplomatic cables posted on the internet by WikiLeaks last month.

However, the unit announced on 12 January that it had killed a 32-year-old man in Dhaka and since then has shot dead three more men in the capital.

According to a report published this month by the Bangladeshi rights group Ain O Salish Kendra, 133 people died in extrajudicial killings in Bangladesh last year; RAB officers were said to be responsible for the overwhelming majority.

Another human rights group, Odhikar, put the figure at 127 and said that 74 died in operations involving RAB. Around 18 of those who died were said to be communist party activists.

Human Rights Watch, the New York-based NGO, has described RAB as a Bangladeshi government death squad, pointing out that senior political figures have expressed support publicly and privately for its policy of extrajudicial killings. The group has called for the UK to withdraw its support.

The leaked diplomatic cables showed that Washington is prevented by law from offering support to RAB because of its human rights abuses. RAB has admitted killing more than 600 people since its inception in 2004. Its use of torture has been documented by the UK government as well as human rights groups.

The British government does not face the same legal restraints as the US government and began offering training in late 2007, around the time that UK intelligence agencies were seeking closer counterterrorism co-operation with RAB and with Bangladeshi intelligence agencies.

Small teams of British police from forces such as West Mercia and Humberside have travelled to Bangladesh under the auspices of the National Police Improvement Agency. The leaked cables show that they offered training in "investigative interviewing techniques and rules of engagement".

Asked whether it believed it was appropriate for British officers to be training members of an organisation condemned as "a government death squad", and whether courses in investigative interviewing techniques might not render torture more effective, an NPIA spokesman said the courses had been approved by the government and by the Association of Chief Police Officers.

The Foreign Office, which funds the programme from its counterterrorism programme, said it was intended to provide "human rights and ethical policing skills training". A spokesperson said: "A decision to fund a particular project is taken only after an assessment of possible impacts and human rights implications has been completed."

Shortly after WikiLeaks posted his confidential cables on the internet, James Moriarty, US ambassador to Dhaka, said every extrajudicial killing should be investigated in a transpararent fashion by the Bangladeshi authorities.

Successive governments have promised to end RAB's use of murder. The current government promised in its manifesto that it would end all extrajudicial killings, but they have continued since its election two years ago.

In 2009 the shipping minister, Shahjahan Khan, speaking in a discussion organised by the BBC, said: "There are incidents of trials that are not possible under the laws of the land. The government will need to continue with extrajudicial killings, commonly called crossfire, until terrorist activities and extortion are uprooted."

Because RAB enjoys popular support in Bangladesh, with some sections of the population even voicing support for the extrajudicial killing of alleged criminals and terrorists, activists at Human Rights Watch and elsewhere argue that it will be disbanded only as a result of pressure from western governments.

The Bangladeshi prime minister, Sheikh Hasina, is visiting the UK, meeting political figures, and is to speak at the Oxford Union. On Monday Lord Howells, the Foreign Office minister, told the Lords that concerns about RAB were "exactly the sort of matter" that David Cameron would be raising when he met her. Meanwhile, the human rights lawyer Phil Shiner is considering mounting court proceedings to challenge the legality of the UK's support for RAB.