"There have been a number of attacks, particularly in the south and east of the country. But we are seeing queues forming at polling stations in the north, also in the capital, as well as, encouragingly, in the east."
About 17 million people are eligible to vote, with 6,500 polling stations open in 364 districts across the country.
There were no reports of any casualties in the Kandahar blasts, but police sources told Al Jazeera that one out of the 55 or so polling stations in the southern city had been hit.
Ahmad Wali Karzai, head of the Kandahar provincial council and brother of Hamid Karzai, the incumbent Afghan president, said that there had been "a very good turnout" across the province.
"There were so many explosions last night and this morning before the polling stations opened," he told Al Jazeera.
"We had serious security challenges, but despite all the challenges we have had a very good turnout and the people of Kandahar came out bravely and voted.
"We are very happy and satisified with the results."
The government regained control of Kandahar city last year, but the south of Afghanistan is still the Taliban heartland.
In the north of the country, Al Jazeera's Hashem Ahelbarra, reporting from the city of Mazar-e-Sharif, said that turnout appeared to have been good early on Thursday.
"We have spoken to election commission officials in different provinces of the north of Afghanistan and we were told that in six provinces out of the nine in the north voter turnout was really high," he said.
"The north of Afghanistan has been described as relatively calm ... and here in Mazar-e-Sharif we haven't seen any incidents so far."
Hamid Karzai was the first of the more than 30 candidates to vote on Thursday, casting in his ballot in a boys' school adjoining the presidential palace.
He urged Afghans to follow his lead and head to the polls in defiance of the Taliban threats.
|Karzai urged voters to defy Taliban threats
and cast their ballots [Reuters]
"I request my dear countrymen to come out and cast their vote to decide their future," Karzai said.
"Vote. No violence."
The Taliban has demanded that Afghans boycott the polls, threatening to cut off the fingers of those who vote and saying they will attack polling stations.
Abdullah Abdullah, a former foreign minister and likely Karzai's closest challenger, thanked voters for going to the polls.
"I am happy that a lot of people are participating in this election despite security concerns and concerns about fraud in the election," he said.
"I hope none of these concerns stop our people from going to the poll, so people can make their own future with their free vote."
A statement from the Taliban on Wednesday said Taliban fighters were closing roads across the country, the Reuters news agency reported.
"... all main and secondary roads will be blocked for traffic and the mujahidin will bear no responsibility for whoever gets hurt," the statement said.
In Kabul on Wednesday, the streets were quiet with shops and businesses closed and police checking the few cars of the roads.
The Nato-led military force in Afghanistan has vowed to make every effort to protect voters, saying that more than 100,000 international troops will refrain from offensive operations on election day.
Polls close at 11:30 GMT, with preliminary results expected by Saturday.
The Afghan government has called for an international media blackout on reporting violence on the day of the election, amid fears that security concerns could keep voters at home.
Opinion polls are indicating a lead for Karzai with 45 per cent of the ballot.
But without an outright majority of 50 per cent, Karzai would be forced into a run-off with his closest challenger, which is expected to be Abdullah Abdullah, his former foreign minister.