Religious studies lecturer Mohammad Hanif said there was a deafening explosion and “everyone in the halls was screaming for help”.
1TV News quoted the health ministry as saying that 24 of the wounded were severely injured.
Afghan President Ashraf Ghani condemned the “terrorist attack”.
The president declared November 21 a day of national mourning, with the flag to be flown at half mast.
The UN mission in Afghanistan tweeted: “UNAMA outraged by #Kabul bombing when communities across #Afghanistan are marking day of special religious significance. Credible reports of heavy civilian casualties. UN human rights teams establishing facts. UN family extends deepest condolences to the many families affected.”
Pakistan’s PM Imran Khan condemned the “cowardly act of terrorism” and sent his condolences to the bereaved families.
The Islamic State in Afghanistan group, sometimes known as Islamic State Khorasan, has claimed responsibility for most of the recent deadly attacks of this kind.
It said it was behind two attacks in Kabul in August that killed dozens of people.
The Taliban have also continued attacks, although many of them target security forces.
A Taliban spokesman, Zabiullah Mujeed, has denied the group had any involvement in November 20 attack.
Afghanistan is voting for a new president in what will be the nation’s first ever transfer of power through the ballot box.
A massive security operation is under way to thwart the Taliban which has vowed to disrupt the election.
Eight candidates are vying to succeed Hamid Karzai, who is barred by the constitution from seeking a third consecutive term as president.
The poll has already been overshadowed by the shooting of two journalists.
Award-winning German photographer Anja Niedringhaus was killed and veteran Canadian reporter Kathy Gannon was injured when a police commander opened fire on their car in the eastern town of Khost on Friday. They had both worked for Associated Press for many years.
It was the latest in a string of deadly attacks that marred the lead-up to the election.
The biggest military operation since the fall of the Taliban in 2001 has been rolled out for the vote. All 400,000 of Afghanistan’s police and soldiers were said to be on duty for the election.
Afghanistan is voting for a new president in what will be the nation’s first ever transfer of power through the ballot box
In parts of the capital voters could be seen queuing an hour before polls opened.
However, some polling stations in the provinces of Herat in the west and Kapisa, north-east of Kabul, were closed because of a combination of the bad weather and security risks. There were also reports elsewhere of several polling centers not receiving ballot materials in time.
Independent Election Commission chairman Ahmad Yousuf Nouristani urged all Afghans to vote, as he cast his ballot live on television.
Traffic was prevented from entering the Afghan capital from midday on Friday, with police checkpoints erected at every junction.
International observers are increasingly optimistic that both the tight security and a number of new guarantees against fraud will make this a fairer election than Afghanistan has seen before.
Afghans have been barred from sending text messages until polls close at 16:00 on Saturday to prevent the service from being used for last-minute campaigning.
But there are still concerns about ballot stuffing and ghost polling stations as well as the fact that the number of election cards in circulation appears to be vastly more than the number of registered voters.
On Saturday the interior ministry said two police were arrested in Wardak province for stuffing ballot boxes.
There are eight candidates for president, but three are considered frontrunners – former foreign ministers Abdullah Abdullah and Zalmai Rassoul, and former finance minister Ashraf Ghani Ahmadzai.
Dr. Abdullah Abdullah has fought a polished campaign, Dr. Ashraf Ghani has strong support among the new urban youth vote and Dr. Zalmai Rassoul is believed to favored by Hamid Karzai.
However, no candidate is expected to secure more than the 50% of the vote needed to be the outright winner, which means there is likely to be a second round run-off on May 28.
A poll conducted by the Free and Fair Election Foundation found that more than 75% respondents planned to vote, even though faith in the electoral process was said to be decreasing.
The headquarters of the Afghan election commission in Kabul have been attacked by insurgents, a week before the presidential election, police say.
Gunmen have entered a nearby building and are firing at the election commission with automatic weapons.
The attack comes a week before presidential elections which the Taliban have vowed to disrupt.
Insurgents attacked the headquarters of the Afghan election commission in Kabul (photo AP)
It comes a day after a major attack on a building housing foreign aid workers in the Afghan capital.
A police officer quoted by Associated Press news agency says the assailants have not entered the heavily secured compound of the International Election Commission and are based in a house about 500 m away.
The insurgents are attacking the commission headquarters with assault rifles and some heavier weapons.
The commission is on a specially built site on a main road out of the centre of Kabul to the east, he adds. It is not yet clear if there are any casualties.
“We heard two explosions inside the IEC compound, the sound of firing is still ongoing, but people are safe and are in (reinforced) safe rooms,” IEC spokesman Noor Mohammad Noor tells AFP news agency.
Pakistani Talibans have attacked an army checkpoint, killing 13 soldiers and 10 civilians, officials say.
The raid took place in the town of Serai Naurang in north-west Khyber Pakhtunkhwa province early on Saturday, and lasted several hours.
Twelve militants were killed in the attack, some of them suicide bombers, the officials said.
Pakistan Taliban says the attack was in response to the death of two commanders in a drone strike last month.
“Pakistan has been co-operating with the US in its drone strikes that killed our two senior commanders, Faisal Khan and Toofani, and the attack on military camp was the revenge of their killing,” a Taliban spokesman said, quoted by Reuters news agency.
Pakistani officials have often been critical of drone strikes, but analysts say that on some occasions it has privately sanctioned such actions.
Pakistani Talibans have attacked an army checkpoint, killing 13 soldiers and 10 civilians
Police officer Arif Khan said between 25 to 30 militants were involved in the attack.
The Taliban said four of the attackers were suicide bombers.
Security sources said the militants were armed with automatic weapons and rocket-propelled grenades, and said they included suicide bombers.
At least eight soldiers were wounded, the sources said.
The 10 civilians, including three women and three children, were killed in a nearby house.
There are conflicting reports about whether the house was hit by a rocket or the militants broke into it.
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