The attack caused panic among troops at the tightly guarded event
Afghan authorities have arrested two men and accused them of involvement in last week's attack on a military parade attended by President Hamid Karzai.
One worked for the defence ministry and the other for the interior ministry, intelligence chief Amrulleh Saleh said.
He said the government still believed that Pakistan-based militants linked to al-Qaeda were behind the attack, which killed three people.
The Taleban said they were responsible. President Karzai escaped unharmed.
Security forces whisked him away as shots rang out. An MP and a 10-year-old child were among the dead.
"Al-Qaeda's role and involvement in the attack is very clear," Mr Saleh told reporters in Kabul on Sunday.
He added that those responsible had bases in Pakistan, where he said they faced "little and sometimes no pressure".
Pakistan, which has seen attacks by militants, says it does all it can to crush al-Qaeda and other militants on its soil.
After the attack, a Taleban spokesman said the group had not targeted Mr Karzai directly, but wanted to show how easily they could get access to such events.
The Taleban have vowed to target Kabul as part of a drive to overthrow the government and expel more than 55,000 foreign troops stationed in the country.