The explosions took place at the entrance of the 400-bed Sardar Mohammad Daud Khan hospital in central Kabul and security forces had been sent to the area, Interior ministry spokesman Qari Saeed Khosty said.
There was no confirmation of casualty numbers but a Taliban security official, speaking on condition of anonymity, said there were at least 15 dead and 34 wounded.
Italian aid group Emergency, which runs a trauma hospital some 3 km from the site of the blast, said nine wounded had been brought in so far.
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 of the city and witnesses said at least two helicopters were flying over the area.
There was no immediate claim of responsibility. But the official 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.
A health worker at the hospital, who managed to escape, 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.
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 hospital in 2017, killing more than 30 people.
The group's attacks have caused mounting worries outside Afghanistan about the potential for the country to become a haven for militant groups as it was when an al Qaeda group attacked the United States in 2001.
The concern has been worsened by a spiralling economic crisis that has threatened millions with poverty as winter approaches.
The abrupt withdrawal of international support following the Taliban victory has brought Afghanistan's fragile economy to the brink of collapse just as a severe drought has threatened millions with hunger.
At least two explosions followed by the sound of gunfire were heard close to the Sardar Mohammad Daud Khan military hospital in the Afghan capital Kabul on Tuesday, a witness who lives nearby said, AzVision.az reports citing Reuters.
Photographs shared by residents showed a plume of smoke over the area of the blasts.
No comment was available from Taliban officials and there was no immediate claim of responsibility.
ISIS, which has carried out a series of attacks on mosques and other targets since the Taliban’s seizure of Kabul in August, attacked the 400-bed hospital in 2017, killing more than 30 people.
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