A suicide bomber struck a crowded market in restive southeast Afghanistan, killing nine people including a senior Afghan commander, while another blast hit a neighbouring province's governor's office.
The two attacks took place in Paktia province and isolated neighbouring Khost, where seven CIA employees and a Jordanian intelligence officer were killed by a suicide bomber last week in the deadliest strike against the US spy agency in decades.
The attacks may signal a deterioration in security in the southeastern area.
In a third attack, also in Khost, a suicide car bomber detonated his vehicle outside a base of Western troops and Afghan police, but caused no casualties.
The Afghan National Department of Security said its members killed five militants, including two would-be suicide bombers, in a separate clash outside Khost's provincial capital.
A security commander allied to foreign troops and three of his bodyguards were among the nine killed in the suicide attack in Gardez, capital of Paktia, said provincial police chief Aziz Ahmad Wardak.
28 people were wounded, including two border police officials, he said.
The apparent targets of the attack were the Afghan security officials allied to foreign troops, said a spokesman for the provincial governor, Rohullah Samoon.
The acting governor of Khost, Tahir Khan Sabri, and several provincial officials were wounded by a blast in Sabri's heavily-guarded office, a possible sign of the insurgents' increasing ability to penetrate areas seen as secure.
In a statement on a Taliban website the militants claimed responsibility for that strike.