Zabihullah Mujahid, a Taliban spokesman, told AP that one suicide bomber targeted the presidential guards who were protecting Ghani and the rally in northern Parwan province along with other members of the security forces.
US Secretary of State Mike Pompeo has condemned the terrorist attacks carried out by the Taliban suicide bombers in Afghanistan in which at least 48 people were killed.
The Taliban claimed responsibility for the attack in a media message from spokesman Zabiullah Mojahid. In 2018, Iran said such talks had taken place in the past and that it would continue to facilitate talks between the insurgents and the Afghan government as part of efforts to bring a negotiated end to Afghanistan's 18-year war. But the rally's location in Parwan, a province north of Kabul that includes Bagram Air Base, had been deemed safe enough for the president to visit in person.
"What he read from the draft outlining the now dropped deal abandoned Ghani and his officers - that had been closed out of the discussions from the Taliban refusal to negotiate with exactly what they believed a illegitimate" puppet" regime - seriously shaken and resentful, said a senior Kabul officer near the Afghan leader.
"The government needs to be on board if there is a deal in the future", the Afghan official said.
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From Ghani's point of view, Taliban assurances that they would not allow militant groups such as Al Qaeda to operate in Afghanistan were worthless, given the formal oaths of loyalty that bound them.
This was the deadliest single day since the peace agreement with Taliban insurgents was terminated. Authorities initially did not give casualty figures, but later said 22 people had been killed and a further 38 wounded.
Earlier on Tuesday, an explosive device purportedly attached to a motorbike hit a campaign rally attended by President Ashraf Ghani.
Security at rallies across the country has been tight following threats by the Taliban to attack meetings and polling stations.
Trump also loosened the US rules of engagement (ROE) in Afghanistan further, no longer requiring USA troops to be in contact with the Taliban before opening fire. The deal aimed to guarantee U.S. military withdrawal from the region in exchange of security and intel agreements.