No one was hurt in the attack in the southeastern province of Paktika on Saturday, but police battled gunmen for hours, delaying the site's opening, Bronwyn Curran, a spokeswoman for the Afghan-UN election body, said on Monday.
She said security and other problems, such as sandstorms and flooding, had prevented registration at 59 of 1052 stations nationwide, but 73,000 people had registered in the first two days of the month-long process that began on Saturday.
More than 10.6 million people registered for October's presidential polls won by Western-backed incumbent Hamid Karzai.
Parliamentary elections are set for 18 September and organisers aim to register up to two million people who were either too young for the October vote, did not previously register, lost their registration cards, or have moved.
Curran called the progress remarkable.
"We are now three days into the voter registration with an overwhelming response," she said. "We are quite well advanced with the electoral process, so despite security problems, we are well on track."
She said several districts of the troubled southern province of Zabul were among those where registration could not take place as helicopters could not fly in.
Afghan and US troops have been
battling the Taliban
Briefing the UN Security Council on Friday, UN Special Representative to Afghanistan Jean Arnault said worsening security had a negative impact on poll preparations.
He said combat operations were not enough to beat rebels' destabilisation strategies and it was necessary to attack their financing, training safe havens, and support networks.
Curran said security was being assessed day by day, but it was not envisaged that a delay in the vote would be necessary.
"Despite the security challenges around Afghanistan and obviously escalating level of violence, none of the key phases of the election have been delayed so far," she said.
French Chief of Defence Staff Henri Bentegeat told a news briefing at the end of a visit to Kabul, France would station six Mirage warplanes in neighbouring Tajikistan from August as part of Western reinforcements to protect the Afghan election.
Registration began after a major anti-Taliban operation last week which the government said killed 178 rebels.
On Sunday, the Taliban said it had lost only seven or eight men, while US military spokesman Colonel Jim Yonts said US estimates were of 77 fighters dead and 13 captured.
"Despite the security challenges around Afghanistan and obviously escalating level of violence, none of the key phases of the election have been delayed so far"
Spokeswoman for the Afghan-UN election body
In the southern province of Helmand, governor Haji Mohammad Wali said troops had caught eight rebels, including two commanders, in a weekend operation involving 450 troops.
He said one was Mullah Fazlulhaq, who he said had recently been appointed Taliban commander for Helmand.
US and Afghan forces have reported killing more than 200 rebels this month and about 400 since March.
While the latest operations appear to have been a blow to the Taliban, it remains to be seen how much damage has been done to it. Analysts say the Taliban has been attracting hundreds of new recruits from Pakistan and elsewhere.