The attack came a day after Taliban fighters created chaos in the centre of Khost, seizing government buildings for several hours.
Al Jazeera's Zeina Khodr, reporting from the Afghan capital, Kabul, said Wednesday's attack was the third outside Camp Salerno in recent months.
"The Taliban have claimed responsibility and, according to the Taliban, they killed a large number of foreign and Afghan forces."
"A US spokesman tells us the Taliban 'dreams of entering the base, but all they're doing is killing Afghans'."
A day earlier, the Taliban distributed leaflets in a nearby mosque, telling Afghans they would be "punished" if they continued to work for a US construction firm which operates inside Salerno.
In Tuesday's attack on the Khost government buildings, fighters barricaded themselves inside and took a number of people hostage.
The government buildings were later retaken by Afghan and US forces.
The Taliban said it had sent 30 suicide bombers to Khost. Eight were killed on Tuesday and one carried out the attack outside Salerno.
"If the Taliban's claims are true, 21 suicide bombers remain in the area, waiting to strike," Khodr reported.
"These are new, sophisticated tactics - to send a group of fighters, armed with weapons and suicide vests, to storm government buildings.
"They are trying to expose the weakness of Afghan security forces and international troops."
Zamary Bashari, an interior ministry spokesman speaking to Al Jazeera, described the security situation in Khost as a "source of concern".
"Khost province is located on the the border with Pakistan and the border there is open. We don't have enough control because of difficult terrain.
"Police forces are protecting the border but there are areas where the enemy can infiltrate into that province.
"We hope that with new measures that the ministry of interior have adopted, we'll be able to provide good security."