The bomb blasts – which left multiple people dead, including US troops, in at least two explosions – came just hours after warnings an attack by an Islamist group may be imminent.
The Ministry of Defence did not confirm or deny whether the so-called Islamic State (IS) splinter cell, Isis-K, was believed to be behind the explosions.
But an anonymous US official said the blasts were “definitely believed to be” carried out by IS.
One explosion took place at or near the Baron Hotel, where the UK has been processing Britons and Afghans eligible for evacuation after the Taliban seized control of the nation.
A second blast occurred a short distance away near the Abbey Gate of Kabul’s airport.
A senior Kabul health official told the BBC that more than 60 people had died in the explosions, while more than 140 people were injured.
The Ministry of Defence said there had been no UK military or Government casualties reported at an early stage – but a US general said 12 US service members have been killed and 15 more have been injured in the attack.
Marine Corps General Kenneth McKenzie, commander of US Central Command, told a news conference: “At this time we know that 12 US service members have been killed in the attack, and 15 more service members have been injured.
“A number of Afghan civilians were also killed and injured in the attack.”
In a tweet, the Ministry of Defence said: “There have been no reported UK military or UK Government casualties following the incidents in Kabul.
“UK forces are working closely with our partners to provide security and medical assistance.”
‘My thoughts are with those bereaved and injured’.
Ms Sturgeon added: ‘We owe such a debt to our armed forces and others working against the clock to evacuate as many people as possible from this grim situation’.