The blast in a crowded area of Ghazni city was the latest in a wave of near-daily attacks by the Taliban, who now hold sway over about half of Afghanistan and continue to intensify attacks on Afghan forces despite increased efforts towards a peace agreement to end the 18-year war.
At least 14 people were also killed and dozens injured in a Taliban mortar attack last Saturday on a busy market in the northern province of Faryab.
The attack came at the onset of a two-day meeting between Afghan citizens and the militants, meant to open the way to a peace process that should build on a hoped-for deal between the United States and the Taliban to end the longest ever USA war.
Suhail Shaheen, the spokesman for the Taliban's office in Qatar, also expressed his satisfaction over the latest round of peace talks with the US. "We have not faced any obstacles yet", he tweeted. The Taliban, he added, have even been talking about the need to reduce violence against women.
U.S. -Taliban negotiations are scheduled to resume on July 9 without any Afghan government representatives. "While they are holding talks in Qatar, every day in Afghanistan they are shedding more blood of innocent civilians", Ghani said.
For the first time since Washington began negotiating with the Taliban past year, two Afghan government officials came face-to-face with Taliban representatives at the intra-Afghan gathering.
He said Washington's "aspiration" is to have that framework in place by September 1 and ahead of the Afghan presidential election scheduled for September 28.
A previously planned meeting between Afghan representatives and the Taliban in April collapsed due to a disagreement over the size of the proposed 250-strong Afghan delegation as well as over its official status.
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"But an agreement that is just between the United States and the Taliban is not a peace agreement for Afghanistan", she said.
An agreement with the Taliban is expected to have two main points - a United States withdrawal from Afghanistan and a commitment by the militants not to provide a base for terrorists, the main reason for the U.S. invasion 18 years ago.
But Wahid Muzhda, a Kabul-based security analyst, told DW it could be risky.
President Donald Trump is impatient to pull the remaining 14,000 USA troops out of Afghanistan, believing nothing more can be achieved from the military operation launched after the September 11, 2001 attacks on the United States.
United States and Taleban officials will reconvene on Tuesday.
"I think we have to accept that through fighting, no one will win, everybody will have to accept peace", Afghani said, calling the event "a big step towards peace".
Zalmay Khalilzad said substantive progress had been made on all four parts of a peace deal: counter-terrorism assurances, troop withdrawal, participation in Intra-Afghan dialogue and negotiations, and a permanent and comprehensive ceasefire.
"They should know that it is not possible to gain privileges in peace talks by targeting civilians, especially children", he said in a statement.