Both groups have warned Afghans against participating in the elections and have used violence to try to prevent people from going to the polls.
Scores of attacks marred the first day of the election on October 20, with an AFP tally showing almost 300 civilians and security forces were killed or wounded in poll-related violence.
The UN-backed government is rife with corruption and many Afghans have said they do not expect the elections to be fair.
With the Taliban operating freely across much of the country and heavy pressure from global partners for the vote to be held, the election was seen as a major test of the credibility of the government.
Independent Election Commission deputy spokesman Aziz Ibrahimi said voting was to start at 7 am.
According to reports, 109 candidates are running for the parliamentary elections from Kandahar province, including 96 men and 13 women.
Residents braved threats of militant attacks to queue on Saturday outside more than 170 polling stations across the province amid heavy security.
IEC figures show roughly 4.2 million out of the almost nine million people registered to vote actually cast a ballot. "They can not find people's names on the voters list".
However, the Independent Election Commission (IEC) promised to open polling centers at 7am as scheduled and to resolve problems with voter lists and the biometric system.
Preliminary results of the elections held on October 20-21 are expected to be announced on November 10, while final results are due by December 20.
Police early on October 29 said a suicide attacker on foot blew himself up near a vehicle outside the office. Another eight people were wounded, he said, although the casualty numbers could rise.
Kandahar is the birthplace of the Taliban and has always been a center of the insurgency that has been waged throughout years of global intervention since the Taliban were toppled during a U.S. bombing campaign in 2001.
The ballot was also marred by lengthy delays at polling stations and allegations of fraud. It had also cautioned teachers not to use schools as voting booths.