Rockets were fired at the presidential palace in the Afghan capital Kabul on Tuesday.
The attack came two days before the country's presidential election.
The first rocket caused some damage inside the heavily fortified palace compound, while the second hit the capital's police headquarters, but caused no casualties, reports Sky News.
Taliban spokesman Zabihullah Mujahid, in a message sent on a mobile phone, claimed the fighters had fired four rockets at the capital. He gave no further details.
On Saturday, militants launched the biggest attack in Kabul since February when a suicide car bomber killed seven Afghans and wounded scores more.
Authorities have ringed the capital with security forces and checkpoints in a bid to prevent bomb attacks.