The blast caused smoke to rise above the city and triggered an alarm in the US Embassy.
Two British soldiers were gunned down on Monday by a man in an Afghan army uniform in southern Afghanistan's Helmand province, officials said in Kabul.
The latest militant assault on the Afghan capital comes as the Taliban intensify their nationwide offensive against the US-backed government in Kabul.
Afghanistan's political district was rocked by violence on Thursday when Taliban terrorists blew up a British embassy vehicle and later gunfire broke out at an army base.
Speaking to ANI, Qatar-based spokesperson of Taliban Suhail Shaheen said, "What do you mean by military role? If they come to Afghanistan militarily and have their presence, I think that will not be good for them, they have seen the fate of military presence in Afghanistan of other countries. So it is an open book for them. And about their help to the Afghan people or national projects, I think that is something which is appreciated."
On Sunday, after 13 years of war, over 500 deaths and over 20 billion, United Kingdom withdrew from Afghanistan. In a touching ceremony, the Union Jack flag was lowered at Camp Bastion, which has been the center of UK operations in Afghanistan since 2006. British Prime Minister David Cameron vowed that Britain will 'never forget those who made the ultimate sacrifice' and Labour leader Ed Miliband said the handover was a "time to remember those who have served Britain so courageously in Afghanistan over the last decade".