Officials say several kidnappers held after police raid in western Kabul.
Later, fighters also fired rockets at a Nato military base in the eastern province of Nuristan on Wednesday,
Two Afghan soldiers were killed and 11 US soldiers wounded, a provincial official said.
Hours later, a Nato convoy was attacked in a rare raid in the relatively peaceful western province of Herat destroying a vehicle, a provincial official said, but he did not know if there were any casualties.
A Nato official confirmed the incident, but also had no information on casualties.
In a separate incident, gunmen abducted a mayor of a southern Afghan town on Wednesday, an official said.
Dur Ali Shah, the mayor of Gereshk, a town in the province of Helmand, was abducted with two of his sons and another man as he traveled to the provincial capital of Lashkar Gah, Abdul Manaf Khan, the Gereshk district chief, said.
The gunmen released his sons and the other man traveling in the car, but kept Shah, Khan said.
Authorities have launched a search-and-rescue operation.
Meanwhile, two boys were killed in a cross-fire as police clashed with Taliban fighters in southern Afghanistan, police said on Wednesday.
The children, from a nomadic tribe, died in fighting in the southern Afghan province of Ghazni where the Taliban are thought to have been holding 19 South Korean hostages for more than a month.
“We’re investigating to find out how those two kids were killed. We don’t yet know if they were killed by police or enemy fire,” Alishah Ahmadzai, the provincial police chief, said.
He said the fighting on Tuesday lasted several hours and a number of Taliban fighters were also killed, although he could not give an exact figure.
Two Taliban fighters died in a separate clash elsewhere in the province on the same day, he said.
In other violence, two policemen and four gunmen were killed in fighting in the eastern province of Paktika.
The violence was the latest in an upsurge of Taliban-led unrest which has plagued Afghanistan since the fighters were ousted by a US-led invasion in late 2001.