"The security forces, as a result of giant operations, overwhelmed and overcame all these attacks and all the bombers were either targeted by security forces or detonated during the exchange of fire," he said.
Earlier, a Taliban spokesman had told Al Jazeera that up to 30 fighters had been sent to attack locations across Khost because of the heavy US military presence in the province.
The third largest US base in Afghanistan is outside the city, which lies just 40km from the border with Pakistan.
The Afghan ministry of defence said that nine Afghans were killed, as well as the suicide bombers, and another 16 people were wounded in the apparently co-ordinated attacks.
The attack started with a suicide bombing outside the governor's compound, where a number of US troops were meeting with the provincial police chief, Brian Naranjo, a US military spokesman, told The Associated Press news agency.
"When the explosion occurred at the governor's compound, they responded and they were engaged with small arms fire," he said.
"Since that initial attack there have been more attacks in Khost."
Bashari told Al Jazeera that the attackers were dressed as Afghan soldiers.
"They were all wearing military uniforms and they had weapons and suicide vests," he said. "This is not the first time this kind of attack has happened in Afghanistan."
Last month, the Taliban released a statement saying that from May 1 it would increase ambushes and suicide attacks on government buildings and officials in response to Washington's decision to send more troops to Afghanistan.
Al Jazeera's Zeina Khodr, reporting from Kabul, said that the Taliban had promised to match US efforts in Afghanistan.
"The Taliban spokesman told us today that this was just the first in a series of attacks planned against government officials, diplomatic missions and military units," she said.
"They even made a call to those who work for the Afghan government, both in the military and government offices, to leave their jobs or they will be targeted."
The US is sending about 21,000 extra troops to Afghanistan as part of the White House's plans to confront the growing power of the Taliban in the region.
The White House plan calls for a military push to reverse deteriorating security, and an increase in civilian aid and development assistance.
Hamid Karzai, the Afghan president, met Barack Obama, his US counterpart, last week in Washington to discuss their joint approach to combat the Taliban in Afghanistan and neighbouring Pakistan.