Chief negotiator Sher Mohammad Abbas Stanikzai insisted negotiation remained "the only way for peace in Afghanistan" during an exclusive interview. Dozens extra get been wounded in the blasts, for which the Taliban claimed accountability.
He also defended the Taliban for taking shelter in civilian homes, and refused to be drawn on the many direct Taliban attacks which had killed ordinary men, women and children.
Peace talks between the United States and the Taliban meant to reach a deal on the withdrawal of thousands of USA troops collapsed last week after President Donald Trump cited an attack that killed a US soldier as his reason for calling off negotiations.
Later, the channel reported an explosion in the Afghan capital Kabul near the US Embassy.
By Ghani's standpoint, Taliban assurances that they wouldn't allow militant groups like Al Qaeda to operate in Afghanistan were unworthy, given the proper oaths of loyalty that bound them.
The talks, which did not include the Afghan government, were intended as a prelude to wider peace negotiations.
"It was a significant collapse of this deal that Khalilzad couldn't convince the Taliban to enter into direct discussion with the Afghan authorities", the Afghan official said.
The two sides had engaged in nine rounds of talks in Doha, Qatar, and a meeting on U.S. soil had been mooted before negotiations failed.
In Parwan, Mujahid said the bomber targeted presidential guards who were protecting Ghani and the rally, along with other members of the security forces. But Aziz said the explosion occurred some distance from where Ghani was addressing a crowd of about 2,200. But the two bombings early on Tuesday were significant for where they happened.
Firdaus Faramarz, spokesman for the Kabul police chief, said Tuesday that 38 others were wounded in the attack that took place near the Massoud intersection.
Many women and children were among the casualties, said Dr. Qasim Sangin, a local official.
The Taliban have stepped up attacks after the breakdown of talks with the US.
Several months of talks between the Taliban and the United States, which backs the Afghan government, collapsed this month.