Interior ministry spokesman Qari Saeed Khosty said the explosions took place at the entrance of the 400-bed Sardar Mohammad Daud Khan hospital.
“Security forces are deployed to the area, there is no information about casualties,” he said in the aftermath of the incident on Twitter.
Taliban spokesman Zabihullah Mujahid later said in a statement published on Twitter that at least seven people outside the hospital, including a child, had been killed, with others injured.
Photographs shared by residents showed a plume of smoke over the area of the blasts near the former diplomatic zone in the Wazir Akbar Khan area in central Kabul.
There was no immediate claim of responsibility. But the Bakhtar news agency quoted witnesses saying a number of Islamic State fighters entered the hospital and clashed with security forces.
The blasts add to a growing list of attacks and killings since the Taliban completed their victory over the previous Western-backed government in August, undermining their claim to have restored security to Afghanistan after decades of war.
Islamic State, which has carried out a series of attacks on mosques and other targets since the Taliban’s seizure of Kabul in August, mounted a complex attack on the 400-bed hospital in 2017, killing more than 30 people.
A health worker at the hospital, who managed to escape the site, said he heard a large explosion followed by a couple of minutes of gunfire. About ten minutes later, there was a second, larger explosion, he said.
He said it was unclear whether the blasts and the gunfire were inside the sprawling hospital complex, the largest military hospital in Afghanistan.