A loud explosion rocked the Afghan capital Kabul near the defence ministry on Saturday, hours after a suicide bomber killed 13 people in the eastern province of Kunar.
The Taliban claimed responsibility for the suicide attack that left 15 people dead and 33 wounded.
Officials from Afghanistan, Pakistan, the United States and China have been pressing for a resumption of the peace process interrupted last year between the Western-backed government in Kabul and the Taliban.
But it remains unclear whether the Taliban, struggling to contain deep internal divisions, will take part.
The hardline militant group has conducted a series of attacks in Kabul and other areas this year and has pressed its military campaign in the southern province of Helmand, where it has forced government troops to pull out of a number of districts.
Earlier on Saturday, a suicide bomber killed a local militia commander and at least 10 others outside the governor's compound in Asadabad, the provincial capital of Kunar, near the border with Pakistan.
Provincial Governor Wahidullah Kalimzai said the bomber rode up on a motorcycle to the entrance of the compound and blew himself up, wounding at least 40 people.
"Most of victims were civilians and children who were either passing by or playing in the park," he said.
There was no immediate claim of responsibility, but the apparent target of the attack, a tribal elder and militia commander named Haji Khan Jan, were among the dead.
He had been closely involved in a number of operations against the Taliban in his district last year.