The militants also set off an improvised explosive device (IED) and fired a rocket on responding police unit that arrived at the scene, resulting a police commander killed and four police officers wounded, the official added.
The attack in the Khuja Omari district was the latest insurgent assault in Ghazni province, which is now largely under Taliban control.
In a separate development, three police constables were killed after Taliban attacked security checkpoints in outer neighborhood of Gardez city, capital of eastern Paktia province Thursday night, according to officials.
The province of Ghazni is located south of Kabul lying along a key route.
Lawmaker Mohammad Arif Rahmani said the attack early Thursday morning in Khuja Omari district killed the district governor, intelligence service director and a deputy police official.
Deputy provincial police chief Ramazan Ali Mohsini said among those killed were Ali Dost Shams, the district governor, seven police officers, and five members of the National Directorate of Security, the country's main intelligence agency.
The Taliban controls large swaths of Ghazni, a strategic province near the border with Pakistan.
Police say Taliban fighters attacked a district compound in central Afghanistan overnight, killing at least six government security forces in several hours of fighting.
However, Tolo News quoted sources as saying that the death toll was more than 10.
The casualty figures are impossible to independently verify because of the remoteness of the area.
"Afghan civilians continue to suffer, caught in the conflict, in ways that are preventable; this must stop now", said Ingrid Hayden, the United Nations secretary-general's deputy special representative for Afghanistan. However, Moseni has also claimed that 45 Taliban were also killed and eight members of the Afghan security forces were wounded.