US Defense Secretary Jim Mattis landed in Kabul on Friday for an unannounced visit to war-torn Afghanistan, adding his weight to a flurry of diplomatic efforts to bring the Taliban to the negotiating table.

Islamic State on Thursday claimed responsibility for a twin bomb attack at a wrestling club in the Afghan capital Kabul the previous day that killed at least 26 people.

The second bomb detonated an hour after a suicide bomber blew himself up inside the sports hall in a heavily Shia neighbourhood, as journalists and security forces gathered at the scene.

Afghan security forces battled militants in Kabul's old quarter Tuesday, with military helicopters firing above a mosque to quell an assault that was launched with a rocket barrage against the capital.

Several gunmen were firing on a training facility overseen by the National Security Directorate -- Afghanistan's intelligence agency -- from a nearby construction site.

The attack on Ghazni, a strategic centre on the main road linking the capital Kabul with southern Afghanistan, has come as a severe blow to President Ashraf Ghani.

Taliban fighters continued to roam Ghazni, torching government offices and in control of several police checkpoints.

Heavily armed Taliban fighters attacked the strategic central Afghan city of Ghazni on Friday, burning police checkpoints and seizing control of parts of the centre before being driven back by US-backed forces, officials said.

Afghan police in Kabul Thursday recovered the bodies of three foreign nationals who they said had been abducted and killed, in the latest incident targeting foreigners in the war-torn capital.

The rockets landed in residential areas "near the mountains in PD5 (police district)" in the west of the city, police spokesman Hashmat Stanikzai said.

The march was triggered by a car bomb in Helmand on March 23 that killed at least 14 people and wounded dozens.

A car bomb killed at least 26 people at a gathering of Taliban and Afghan armed forces in the eastern city of Nangarhar on Saturday, an official said, as soldiers and militants celebrated an unprecedented Eid ceasefire.