Eight people were killed in fighting between security forces and suspected Taliban fighters, including a civilian in a US air strike in the run-up to Afghanistan's landmark elections, officials said on Sunday.
The attacks included a bomb blast which killed a French soldier near the Pakistani border and a rocket strike on a UN warehouse on the outskirts of Kabul which left a UN employee with minor injuries.
The soldier was the first French military man to die in Afghanistan.
A second soldier in the same vehicle was seriously wounded in the attack, a statement said, adding that the troops were part of France's contribution to the US-led operation in the country.
Taliban spokesman Abd al-Latif Hakimi told Aljazeera's correspondent in Islamabad on Sunday that the rebel movement had launched a total of 32 attacks across 13 provinces, a claim that cannot be independently verified.
Earlier, an Afghan civilian was killed overnight when US-led coalition forces came under attack in the eastern province of Khost and called in air support to bomb the area, Khost's deputy police chief Muhammad Zaman said.
"One civilian's residence in Khalsas district was also bombed, which resulted in the one civilian death. Five people from the same house were wounded," Zaman said.
The US military said it was checking the report.
But officials maintain that the situation was under control and that people who had wanted to vote had been free to do so.
The polls were held nearly four years after US-led forces invaded Afghanistan and drove the Taliban from power.
"The voting process is ongoing as normal in the district," Khost police chief Muhammad Ayub said.
"There was a small fire, one local staff member was slightly injured"
UN spokesman Adrian Edwards
A poll official said a rocket blast at a UN compound in Kabul wounded a staff member.
"There was a small fire, one local staff member was slightly injured," said UN spokesman Adrian Edwards.
In another incident, a security post in the eastern province of Khost came under fire overnight, killing two policemen and wounding two US soldiers and an Afghan soldier, the police chief said.Afghan President Hamid Karzai said Afghans were making history in determining their future after 30 years of war and foreign interference.
Three alleged Taliban fighters were killed in the ensuing firefight in the Yaqubi district, 130km southeast of the capital Kabul, Ayub said."Their bodies are still at the site," he added.
Afghan security forces had surrounded the area and were searching the area, he said. The clash had not affected polling, he said.
Separately, a suspected fighter was killed in an assault on a polling station late on Saturday in the southern province of Helmand, provincial governor Mullah Shir Mohammed said.
And a French special forces soldier was killed by a bomb blast in southern Afghanistan in the early hours of Sunday, said the French chief of general staff in Paris.
No further information was provided by the French military.
"[It] is the day of self-determination for the Afghan people," said Karzai, who won a presidential election in October.
President Hamid Karzai said
Afghans were making history
"That is why we are making history after 30 years of wars, interventions, occupations and misery.
"Today Afghanistan is moving forward, making an economy, making political institutions, and today we are completing the Bonn process, completing the laying down of the Afghan state," he said, referring to an international plan for democratisation drawn up after the 2001 overthrow of the Taliban.
About 12.5 million Afghans are registered to vote in the $159-million, UN-organised elections for a lower house of parliament and councils in all 34 provinces.
Some queued from early in the morning at about 6000 polling centres nationwide.
"I came early to take my turn," said Qari Salahuddin, 21, waiting with about a dozen other people outside a polling station in the eastern city of Jalalabad.
"We are very happy. I am so happy, I couldn't sleep last night and was watching the clock to come out to vote."
The chairman of the Afghan-UN election commission, Bismillah Bismil, urged Afghans to come out to vote, stressing that the ballot was secret.
"We pray to God that today we have a peaceful, stable and acceptable election," he said. "As we have repeatedly said, your vote will be secret ... only God will know who you voted for."
But Aljazeera's correspondent in Afghanistan, Wali Allah Shahin, reporting from Kandahar, said the voter turnout in the city was poor.
He also cited sources as saying that turnout was even poorer in outlying districts.
Residents told Shahin that they felt the parliamentary elections were not as decisive as the presidential polls last October, and the Taliban's threats had forced some people to stay at home.
"We pray to God that today we have a peaceful, stable and acceptable election"
Bismillah Bismil, chairman, Afghan-UN election commission
The voting system chosen by the government - with candidates standing as individuals, not as part of a party list - has resulted in about 5800 candidates for the two votes.
Women, who make up about 10% of the candidates, have been reserved 68 seats in the lower house, known as the Wolesi Jirga, or House of the People.
Polls closed at 4pm (1130 GMT) although voters in queues at that time will be allowed to vote.
Security, especially in the south and east where Taliban fighters are most active, has been the main worry, and about 100,000 troops, including about 20,000 from a US-led force and 10,000 Nato-led peacekeepers, are keeping guard.
Aljazeera's Shahin said the streets of Kandahar were deserted, with only security vehicles visible.
More than 1000 people have been killed this year - most of them fighters, but also 49 US soldiers - the bloodiest period since US-led forces invaded Afghanistan and overthrew the Taliban.