KABUL, Afghanistan — It was a particularly bloody Wednesday for Afghan police officers, as reports emerged that at least 22 had been killed in four assaults around the country by Taliban insurgents, who also pinned down 40 police officers and officials in a bunker, short on food and ammunition.

The insurgents boasted that their spring offensive was well underway, and said it proved they could disrupt the upcoming runoff election for president of Afghanistan — something they failed spectacularly to do in the first round, on April 5.

In the worst-hit place, in northern Badakhshan Province, some Afghan officials complained bitterly that the American military failed to rescue them, despite an official plea for help.

Officials of the American-led military forces disputed that complaint, but the disagreement highlighted the changed nature of the war as the United States and its NATO allies prepare to leave the country at the end of this year. Their forces have largely stood down from the fight already, turning over security duties to the Afghanistan government.