An attack targeting the Afghan acting defense minister's house in Kabul left at least eight people dead and 20 wounded, the Interior Ministry said on Wednesday.
Taliban militants claimed responsibility for the attack. A Taliban spokesman said more attacks against top government officials were being planned.
The attack comes as the insurgent group presses ahead with an offensive across Afghanistan, seizing several provincial capitals.
Another blast near the office of Afghanistan's main security agency wounded three people on Wednesday. It was not immediately clear if it was linked to the Taliban-claimed attack.
Zabihullah Mujahid, a Taliban spokesman, said the attack was "the beginning of the retaliatory operations" against the Afghan government that ordered attacks against the militant group.
The threat came after Afghan forces launched a counterattack against the insurgents in the southern city of Lashkar Gah.
US and Afghan forces have recently intensified airstrikes against the Taliban to push them back.
Acting Defense Minister Bismillah Mohammadi said in a video released shortly after Tuesday's attack that it would not "have any impact on my willingness to defend my countrymen and my country."
Since foreign troops began their withdrawal from Afghanistan in May, the Taliban made significant advances, especially in rural areas of the country.
On Tuesday, Afghan officials said the Taliban had seized nine out of 10 districts in Lashkar Gah, the capital of Helman province.
Fighting has also been ongoing for days in the Kandahar province and in the western part of the city of Herat, in the west.
The conflict has killed dozens of civilians and displaced hundreds in recent weeks.
Tuesday's attack represents a major escalation by the Taliban as Kabul has largely been spared the violence hitting other parts of the country.