Car bomb kills dozens in Afghanistan

• NEW: Taliban claim a fatal attack in Kabul on a vehicle carrying presidential palace employees


• A car bomb at a market in Paktika province killed at least 38 people, police say


• The device was detonated by a suicide bomber, a police official says


• Afghanistan continues to face major security challenges

Kabul, Afghanistan (CNN) -- A car bomb exploded in a busy market in eastern Afghanistan on Tuesday, killing at least 38 people and wounding 30 others, police said.

The car was driven by a suicide bomber who detonated explosives after police ordered him to stop his car, said Nissar Ahmad Abdulrahimzai, deputy police chief of Paktika province.

Abdulrahimzai said he feared the death toll would rise.

Meanwhile, in the capital, Kabul, the Taliban claimed responsibility for an attack early Tuesday on a vehicle used by presidential palace employees.

Taliban spokesman Zabihullah Mujahid said in a statement to media that three people were killed and six others injured in the explosion.

Hashmatullah Stanekzai, a spokesman for the Kabul police chief, earlier told CNN that at least two people were killed and five injured. He said all the victims were working in the presidential palace media department.

Security remains a major concern in Afghanistan, from which the United States is due to withdraw most of its troops by year's end.

The latest violence comes amid disputes over the country's recent presidential election.

During a visit to Kabul on Saturday, U.S. Secretary of State John Kerry announced that an audit of votes would be carried out to decide the outcome of the election.

Both candidates, Abdullah Abdullah and Ashraf Ghani, have alleged large-scale vote fraud and manipulation during the runoff last month.