Earlier, the Taliban said it was behind the killing of a senior Supreme Court official in the capital, Kabul.
Meanwhile, Nato said two of its soldiers were killed in an insurgent attack close to the main international base to the north of Kabul.
The incidents come amid an upsurge of Taliban violence as the US and Nato mission in Afghanistan nears its end.
The majority of foreign forces leave the country in less than three weeks, although about 12,000 Nato soldiers will remain to train and advise Afghan security forces from 1 January.
In a statement, Nato said two of its soldiers died "as a result of an enemy forces attack" near the Bagram air base in Parwan province near Kabul. The nationality of the soldiers was not released.
The deaths are the first foreign troops killed this month, bringing to 65 the total number of international troops killed in the country this year, 50 of them from the US.
The attacks come just two days after a teenage suicide bomber blew himself up in the auditorium of a French cultural centre in Kabul during a performance of a play condemning violence. One German national was killed and 16 people were injured.
Last month, Kabul's police chief resigned following several attacks on foreigners and locals in the city.
The BBC's Mike Wooldridge in Kabul says the violence has provoked fresh debate about how the Taliban have been able to evade the apparently rigorous security in the capital.
President Ashraf Ghani, who took power in September, has vowed to bring peace after decades of conflict.
