A Taliban spokesman said fighters were attacking embassies in the diplomatic enclave, Nato’s HQ and the parliament building in the west of the capital.
Multiple blasts and gunfire have been heard across Kabul.
The Taliban spokesman said there were also attacks in Logar and Paktia provinces. There are also reports of suicide attacks in Jalalabad.
Smoke billowing
At least seven large explosions were heard in central Kabul and gunfire erupted from various directions in the heavily barricaded diplomatic zone.
Residents were reportedly running for cover and sirens wailing in the Wazir Akbar Khan district.
Some explosions were also heard near the parliament building in western Kabul and police said it was under attack.
A parliamentary spokesperson told Reuters rockets had been fired at parliament and the Russian embassy.
Smoke was said to be billowing from the direction of the German embassy.
The Agence France-Presse news agency reports that the newly built Kabul Star hotel is on fire.
Its reporters said they heard the US embassy sounding alarms and warning staff to take cover.
There are also reports of gunfire from a number of other parts of the capital.
The BBC’s Bilal Sarwary in Kabul says there are also reports of a suicide attack that has closed the centre of the eastern city of Jalalabad.
Police said suicide bombers had attacked the airport there.
There is normally a surge in the number of Taliban attacks at this time of year following a relative lull in winter, when militants find it more difficult to move around.