The insurgents have been meeting with the United States envoy in Doha to hammer out a deal that would see the U.S. military quit Afghanistan in return for various guarantees. The talks are set to resume on Tuesday.
He said Washington's "aspiration" is to have that framework in place by September 1 and ahead of the Afghan presidential election.
The attack came one day after the top USA negotiator in peace talks with the Taliban, Zalmay Khalilzad, told a group of journalists that the past several days of talks with the insurgents had been "the most productive" since such talks began in September, and that "substantive progress" had been made on the four major issues: withdrawal of foreign forces, Taliban anti-terror guarantees, permanent cease-fire and negotiations among Afghans.
Sunday's attack comes amid peace talks between the Taliban and the Afghan government underway in Qatar.
"Essentially the four items we have been talking about ever since we started (are) terrorism, withdrawal of foreign troops, inter-Afghan negotiations and dialogue, and ceasefire", Khalilzad told AFP.
Afghani, in a bid to encourage women's education in post-Taliban Afghanistan, worked with more than 6,000 Islamic scholars in 22 provinces to educate them on women's rights. "We have not faced any obstacles yet".
Sponsored by Qatar and Germany, the two-day talks in Doha are attended by Taliban representatives and about 50 Afghan politicians and activists, including 10 female delegates.
"Afghans meeting with the Taliban was a big success".
Afghan President Ashraf Ghani condemned the attack in a statement, labeling it a "crime against humanity" that proved them to be the enemy of the people.
Observers have criticised the U.S. for allowing its own talks with the Taliban to proceed without the formal participation of the Afghan government, which the Taliban label Washington's puppet.
Sunday's gathering will be the third such meeting following similar summits in Moscow in February and May.
An agreement with the Taliban is expected to have two main pillars - a United States withdrawal from Afghanistan and a commitment by the militants not to offer sanctuary to extremists.
The United States, which by some estimates has spent $1 trillion in Afghanistan, will likely try to insist in the deal that the Taliban open negotiations with Ghani's government. But the thorny issues of power-sharing with the Taliban, the role of regional powers including Pakistan and India, and the fate of Ghani s administration remain unresolved.
Wary representatives of Afghan society met Taliban officials in Qatar on Monday for a second day of talks, with bloody insurgent attacks back home casting a pall over efforts to end Afghanistan's years of war. Sunday's blast killed at least 12 people, including civilians, and injured more than 180 others.
Last fall, Taliban fighters seized large areas of Ghazni province's Malistan and Jaghori districts in fighting that killed hundreds on both sides and displaced thousands of civilians.
"We are happy with progress and hope the rest of the work is also done".
"These six days have been the most productive of the rounds we've had with the Talibs", Khalilzad said in Qatar.
"We have told Iran that we don't want the issues we have with them to have a negative impact on peace in Afghanistan", Khalilzad said.