The insurgents have vowed a campaign of violence to disrupt the ballot on April 5, urging their fighters to attack polling staff, voters and security forces in the run-up to election day.
Five people were killed when the insurgents stormed an office of the Independent Election Commission (IEC) in the west of the capital.
Elsewhere, five civilians were killed in a suicide bombing in northern Kunduz province, while a militant attack on a bank in eastern Kunar also left five dead.
"At around 11:35 am (local time)(1235 IST) a suicide bomber blew himself up at the gate of an IEC regional office in Darulaman, and then several other attackers entered the building," Kabul police spokesman Hashmat Estanakzai said.
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The dead included two policeman and a provincial council candidate, the interior ministry said in a statement. Five attackers were killed by security forces, according to ministry spokesman Sediq Sediqqi.
The attack was close to the home of Ashraf Ghani, who is seen as a frontrunner in the race to succeed President Hamid Karzai.
The Kunduz blast came at a venue where another leading presidential candidate, Abdullah Abdullah, is due to hold a rally on tomorrow, provincial police spokesman Sayed Sarwar Hussaini said.
Three gunmen struck in the attack on the Kunar bank, provincial governor Shuja-ul-Mulk Jalala said, as police lined up to collect their pay.