KABUL, Afghanistan — Insurgents killed at least 15 people in three separate attacks in Afghanistan on Wednesday, and six policemen died in an airstrike for which officials blamed the American military, illustrating the precarious security situation in a country wracked by years of fighting.

The attacks came a day after two rural northern districts fell to the Taliban, expanding the territory controlled by that militant group.

Gunmen and suicide bombers launched what appeared to be simultaneous assaults in the capital, Kabul — one close to the offices of the Asian Development Bank, in the downtown Shar-e Naw neighborhood, and the other in the western part of the city at a police headquarters. Those attacks killed at least seven people and wounded 17 others, according to Wahidullah Majroh, the spokesman for the Afghan Public Health Ministry.

The Islamic State militant group claimed responsibility for the attack on the Kabul police station, and a spokesman for the Taliban said it had carried out the strike near the Asian Development Bank. The Taliban and the Islamic State are deadly enemies of the government — and of each other.