At least seven people have been killed in the crowds near Kabul airport, Britain's ministry of defence said on Sunday.
This comes as thousands of people try to flee Afghanistan and the threats posed by a new Taliban regime, FRANCE24 and AFP report.
"Our sincere thoughts are with the families of the seven Afghan civilians who have sadly died in crowds in Kabul," the UK defence ministry said in a statement on Sunday.
"Conditions on the ground remain extremely challenging but we are doing everything we can to manage the situation as safely and securely as possible."
Tens of thousands of Afghans were still racing to flee on Sunday as the United States warned of security threats at Kabul's airport gates.
At least 20 people have been killed in and around the single-runway airfield since last Sunday, a NATO official said Sunday.
But terrified Afghans continue to try and flee, deepening a tragedy at Kabul airport where the United States and its allies have been unable to cope with the huge numbers of people trying to get on evacuation flights.
Britain's Sky News on Saturday aired footage of at least three bodies covered in white tarpaulin outside the airport. It was not clear how they had died. Sky reporter Stuart Ramsay, who was at the airport, called the deaths "inevitable" and said people were being "crushed" while others were "dehydrated and terrified".
Families hoping for a miracle crowded between the barbed wire that surrounds an unofficial no man's land separating the Taliban from US troops. Roads to the airport were choked with traffic.
US President Joe Biden has described the situation as "one of the largest, most difficult airlifts in history".
Circumstances were further complicated on Saturday when the US government warned its citizens in Afghanistan to avoid travelling to Kabul airport, citing "potential security threats" near its gates.
"We are advising US citizens to avoid traveling to the airport and to avoid airport gates at this time unless you receive individual instructions from a US government representative," the alert from the US embassy in Kabul said.
The warning gave no further details but a White House official later said aides had briefed Biden on local "counterterrorism operations", including against the Islamic State group.
As thousands of Americans and Afghans wait at the airport for flights or gather nervously outside its gates, there have been "sporadic" reports, confirmed by the Pentagon, of Taliban fighters or other militants beating and harassing people trying to flee.
The Biden administration said Sunday that commercial aircraft would be marshalled to help ferry people who have been evacuated from Afghanistan under the Civil Reserve Airfleet agreement – a partnership between the aviation industry, the Defense Department and the US Department of Transportation.
A Pentagon spokesman said the 18 aircraft – including from United, American Airlines, and Delta – would not fly into Kabul but be used to transport people who have already left Afghanistan.
Biden will provide an update on Sunday on the evacuation of American citizens and refugees from Afghanistan, the White House said. The president is to speak at 4pm EDT (2000 GMT), after meeting with his national security team to hear intelligence, security and diplomatic updates on the evolving situation in Afghanistan.
The US military said an Afghan woman gave birth aboard an Air Force C-17 upon landing at Ramstein Air Base in Germany after experiencing complications during the flight on Saturday. The military’s Air Mobility Command tweeted that airmen helped during the delivery of the child in the cargo bay of the aircraft. "The baby girl and mother were transported to a nearby medical facility and are in good condition," a later tweet said."