It was the second suicide bombing in the Afghan capital in 24 hours and the seventh major assault in Afghanistan since Tuesday, taking the total death toll to more than 200, with hundreds more wounded.
The attack comes after a suicide bomber blew himself up in a mosque in Kabul on Friday, killing 56 people and wounding 55 others in an assault claimed by the Islamic State group.
There was no immediate claim of responsibility for the ambush but the Taliban has been involved in the previous four attacks on police and military bases this week.
"This afternoon when a minibus carrying army cadets was coming out of the military academy, a suicide bomber on foot targeted them, martyring 15 and wounding four," defence ministry spokesman Dawlat Waziri told AFP.
Kabul Crime Branch chief General Mohammad Salim Almas said police have launched an investigation into the attack which happened in the west of the city.
"The minibus was carrying army trainees to their homes from Marshal Fahim military academy," Almas told AFP.
The spate of deadly attacks underscores deteriorating security across Afghanistan as the resurgent Taliban step up their attacks on security installations with devastating effect and Islamic State continue to target Shiite mosques.
NATO's Resolute Support mission tweeted that the latest incident was an "attack on the future" of Afghanistan and its security forces.
"This attack in #Kabul shows the insurgents are desperate and cannot win" against Afghanistan's security and defence forces, it said.
In the deadliest of the recent attacks, around 50 Afghan soldiers were killed in a Taliban-claimed assault on a military base in the southern province of Kandahar on Thursday.
Insurgents blasted their way into the compound using two explosives-laden Humvees -- a tactic used in three separate attacks this week -- officials said.
The militants razed the base in the Chashmo area of Maiwand district to the ground, according to the defence ministry.
On the same day Taliban militants besieged a police headquarters in the southeastern province of Ghazni, attacking it for the second time this week.
Afghan security forces have faced soaring casualties in their attempts to hold back the insurgents since NATO combat forces pulled out of the country at the end of 2014.
Casualties leapt by 35 percent in 2016, with 6,800 soldiers and police killed, according to US watchdog SIGAR.
The insurgents have carried out more complex attacks against security forces in 2017, with SIGAR describing troop casualties in the early part of the year as "shockingly high".
The attacks included assaults on a military hospital in Kabul in March which may have killed up to 100 people, and on a base in Mazar-i-Sharif in April which left 144 people dead.
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