The blasts reportedly occurred in the capital city of Afghanistan near the US Embassy, shortly after midnight on 9/11 anniversary.
Violence in Afghanistan has been escalating amid the talks between the United States and the Taliban movement, which has in recent days conducted a number of terrorist attacks that have killed dozens of people in the war-torn country.
On Monday, US President Donald Trump said that US peace talks with the Taliban were dead after the group claimed responsibility for the attack that killed a US service member in Kabul on 5 September.
Afghan President Ashraf Ghani has reiterated, however, his commitment to the people-owned peace process amid the breakup of the US-Taliban peace talks. In turn, the Taliban has vowed to continue fighting against American forces in Afghanistan after the US president withdrew from peace talks with the group.