Foreign Ministry Spokesman Saeed Khatibzadeh deplored the attack, describing it as a terrorist act by the enemies of peace and stability in Afghanistan given the upcoming intera-Afghan talks.
A roadside bomb in Kabul targeted Saleh on Wednesday morning, his spokesman said, but he escaped the attack unharmed.
Initially, Interior Ministry spokesman Tariq Arian said at least two civilians died but the death toll later rose to 10. The ministry said at least 15 people were wounded.
The Taliban, who have pledged not to launch attacks in urban areas under a deal with the United States, denied responsibility.
In a video posted on Facebook soon after the explosion, Saleh, with bandages on his left hand, said he had been travelling to his office when his convoy was attacked.
"I am fine but some of my guards have been wounded. My son, who was in the car with me, and I are both fine," Saleh said.
"I have some burns on my face and hand. The blast was strong."
Saleh, a former intelligence chief and an outspoken Taliban critic, has survived several assassination attempts, including one on his office last year ahead of presidential elections that killed 20 people.
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