More than 522,000 people have registered to vote at the 173 polling stations across Kandahar, according to the Independent Election Commission (IEC).
“I have to vote for a better future for my country,” Abdul Abbas, a shopkeeper, told AFP news agency outside a polling centre.
“I have defied all the threats of attacks and explosions to vote,” he added.
The electoral body said 111 candidates are vying for 11 seats in parliament from southern Kandahar in the country’s 250-seat chamber.
IEC figures show around four million people voted in last weekend’s parliamentary election that was held in 32 out of 34 provinces after months of chaotic preparations.
That compares with nearly nine million on the voter roll, but many suspect a significant number of those were based on fake identification documents that fraudsters planned to use to stuff ballot boxes.
Organisers are under pressure to avoid last weekend’s debacle that forced the IEC to extend the nationwide ballot by a day.
Problems with untested biometric verification devices, missing or incomplete voter rolls and absent election workers following Taliban threats to attack the ballot forced Afghans to wait hours outside polling stations, many of which opened late or not at all.
Elections in the province were postponed after the October 18 killing of General Abdul Raziq, an anti-Taliban strongman seen as a bulwark against the Taliban in the south, amid fears of violence flaring up.
Raziq was among three people killed in an insider attack on a high-level security meeting in Kandahar city that was attended by General Scott Miller, the top US and NATO commander in Afghanistan.
Miller escaped unhurt, but US Brigadier General Jeffrey Smiley was among 13 people wounded in the shooting claimed by the Taliban.
Meanwhile, voting is yet to take place in Ghazni because of the fragile security situation in the province, significant parts of which are under Taliban control.
There is also an ongoing dispute over how to divide Ghazni’s electoral constituencies to have a more balanced ethnic representation.
The IEC is scheduled to release preliminary results on November 10.