Tens of thousands of Americans and Afghans who collaborated with US forces remain stranded in Kabul, as the US government grappled with an overwhelming backlog of visas and Taliban checkpoints which were preventing people safely reaching the airport.

With the 31 August deadline looming, tens of thousands of people eligible for evacuation were yet to be airlifted out, many who were among the crowds gathered around Kabul airport brandishing their papers or proof they had worked on US bases.

The urgency of the evacuation of those allied with US and Nato forces, and western media organisations, was further compounded by growing reports of Taliban fighters going door-to-door looking for those who had worked with the previous regime, and threatening them into joining the Taliban.

A German broadcaster said a family member of one of its reporters had been shot and killed by the Taliban when they came looking for the journalist, who had already fled the country.

This manhunt was despite the Taliban promising just days ago that they would seek “no revenge” and that “nobody will go to their doors to ask why they helped”.

Taliban fighters and their checkpoints continued to blockade the airport on Thursday, major barriers for Afghans who fear that their past work with westerners makes them prime targets for retribution. Prior to Afghanistan falling to Taliban control, more than 300 Afghan interpreters and their relatives were killed by militants because of their US ties, according to the non-profit organisation No One Left Behind.

Hundreds of Afghans who lacked any papers or clearance for evacuation also congregated outside the airport, adding to the chaos that has prevented even some Afghans who do have papers and promises of flights from getting through.

The White House said early on Friday that about 9,000 people had been evacuated since 14 August. Earlier, the US state department spokesperson Ned Price said in Washington that 6,000 people were cleared for evacuation Thursday and were expected to board military flights in coming hours. That would mark a major increase from recent days but was still not at the 5,000 to 9,000 per day evacuation capacity the US said was possible with the available military aircraft.

Only around 2,000 passengers have been flown out by the US on each of the past two days, due to the obstructions around the airport. Pentagon spokesperson John Kirby said efforts were under way to speed up the processing, including bringing in more staff to vet visa applications and opening up additional entry gates at the airport.

Even before Afghanistan fell under full Taliban control, the US had been grappling with a huge backlog in processing Special Immigrant Visas for those who had helped the US military in Afghanistan, due in part to coronavirus halting operations for months. Earlier this year, 18,000 Afghan allies and 53,000 family members remained in the processing backlog.

There is no accurate figure of the number of people – Americans, Afghans or others – who are in need of evacuation as the process is almost entirely self-selecting. It is estimated to be around 11,000 to 15,000 US citizens and dual US-Afghan citizens along with family members, as well as tens of thousands of Afghans who may also be at risk.

Compounding the uncertainty, the US government has no way to track how many registered Americans may have left Afghanistan already. Some may have returned to the United States but others may have gone to third countries.

Democratic Representative Seth Moulton, a former Marine who served four tours in Iraq, called the Biden administration’s efforts to evacuate US citizens and Afghan allies out of the country the “greatest foreign policy disaster that we’ve seen in a very long time”.

Fears were growing for the safety of those stranded. A report by a Norwegian intelligence group said the Taliban had begun knocking on the doors and rounding up Afghans on a blacklist of people who had collaborated with the previous regime.

German public broadcaster Deutsche Welle said the Taliban shot and killed a family member of one of their reporters in Afghanistan and severely injured a second family member.

The broadcaster said in a statement on Thursday that Taliban fighters were looking for the Deutsche Welle reporter and searching homes in western Afghanistan. It said other family members managed to escape. Deutsche Welle said the reporter himself, whose identity was not revealed, was already based in Germany.

Complaints by some Afghan journalists have also cast doubt on assurances that independent media would be allowed.

Meanwhile in the UK, foreign secretary Dominic Raab is facing mounting pressure to resign over his handling of the crisis as the opposition Labour party warned there had been an “unforgivable failure of leadership” by the British government.

The party has set out a list of 18 urgent questions for the foreign secretary to answer about his trip and his department’s handling of the crisis.

Raab, who rejected calls to resign on Thursday, was reportedly “unavailable” when officials in his department suggested he “urgently” call Afghan foreign minister Hanif Atmar on 13 August – two days before the Taliban marched on Kabul – to arrange help for those who supported British troops.

It was reported on Thursday that the Afghan foreign ministry refused to arrange a call with a junior minister, pushing it back to the next day. It has since emerged that a call never took place.