"The latest reports that we have is that Taliban forces are now holed up inside the municipality building in the centre of Khost city. They are surrounded by American special forces and Afghan security forces," she said.
"We are getting reports from government officials in the area that they are holding hostages. We still can not confirm whether they are civilians or government employees.
"It is a very big blow to the Afghan security forces.
"Two car bombings struck outside the governor's office as well as at a police headquarters in the city.
"There were fierce gun battles between the Taliban and Afghan security forces."
The unnamed spokesman said that Khost had been targeted because of the heavy US military presence there.
The third largest US base in Afghanistan is outside the city, which lies just 40km from the border with Pakistan.
Al Jazeera's Khodr said that locations in other areas of the province had also been targeted.
"There have been four to five suicide bombers targeting a number of locations in Khost province," she reported.
Khodr said that the Taliban had been able to gain greater foothold in Khost because tribal leaders in the area were turning away from the government.
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 thousands more troops to Afghanistan.
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 for Afghanistan 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 fighting the Taliban in Afghanistan and neighbouring Pakistan.