KABUL, Afghanistan (AP) — The Taliban completed their sweep of Afghanistan's south on Friday, taking four more provincial capitals in a lightning offensive that brought them closer to Kabul just weeks before the U.S. is set to officially end its two-decade war.

In the last 24 hours, the country's second- and third-largest cities — Herat in the west and Kandahar in the south — have fallen to the insurgents, as has the capital of the southern province of Helmand, where American, British and NATO forces fought some of the bloodiest battles of the conflict.

The blitz through the Taliban's southern...