One car bomb blast in Dasht-e Barchi, a heavily Shi'ite Muslim area of western Kabul, killed a civilian and wounded six, interior ministry spokesman Qari Sayeed Khosty said in a tweet.
There was no confirmation of casualty numbers and one Taliban official, who spoke on condition of anonymity, said seven people had been killed and nine wounded.
A second explosion was also reported in the nearby Karte 3 area, local residents said.
Zabihullah Mujahid, deputy minister for culture and information in the Taliban-led government, told The Associated Press that an investigation was continuing into the incident.
He said that one of the explosions in western Kabul destroyed a minivan. Images from one of the sites showed a disfigured silver van with its windows blown out.
No one has yet claimed responsibility for the explosions. The incident is the third explosion in Kabul over the last week; on Monday a roadside bomb struck a taxi wounding two people.
The Islamic State group claimed responsibility for a blast that killed one person and wounded five others on Sunday.
The attacks have often targeted a neighbourhood of Kabul populated largely by people from the Hazara Shiite minority.
The incident comes as the country is struggling with rising poverty in the aftermath of the Taliban takeover in August.
On Wednesday morning, the Taliban foreign ministry issued a statement calling on the US congress to release Afghanistan’s assets. The funds have been blocked ever since the Taliban took over the country.
“American sanctions have not only played havoc with trade and business but also with humanitarian assistance,” the statement said.
In light of the deteriorating situation, the World Food Program warned this week that 8.7m people in Afghanistan are at risk of facing “famine-like conditions” and an additional 14.1m are suffering acute food insecurity.