The last bomber attacked another police building, but it was not immediately clear if he died when he detonated his explosives or whether he had been killed by police.
A candidate in Afghanistan’s upcoming presidential election was in one of the buildings at the time of the attack, but escaped unharmed.
A Taliban spokesman said that the group’s fighters had staged the attack, but claimed that that they were targeting the courthouse rather Ramazan Bashardost, a former planning minister.
Al Jazeera’s James Bays, reporting from the capital Kabul, said the attackers were “using a tactic we have seen a number of times recently, including during an attack in Gardez a couple of days ago – that’s attackers – male attackers – wearing female burqas to cover themselves and to cover the bombs they have strapped to their bodies.”
He said that there was no clear information on casualties so far.
“One report says that a young Afghan child may have been killed. That’s not confirmed yet,” Bays said.
General Mohammad Zahir Azimi, the defence ministry spokesman, said: “There are casualties but at this moment we don’t know exactly how many people have been killed and injured.”
Khost has become one of the most dangerous cities in Afghanistan over the last six months and the scene of repeated deadly attacks.
Nine people were killed in the attack in the eastern city of Gardez on Tuesday.
Afghanistan has scheduled elections for August 20, but with growing violence across large parts of the country and Afghan and international forces seemingly unable to ensure security, there are fears that few voters will turn out.