KABUL—The number of insurgent attacks in Afghanistan in the three months through June was 11% higher than last year, the U.S.-led coalition here said, an increase that comes after almost a year of declines and provides fuel for the debate about whether the Taliban are regaining momentum as American forces withdraw.

Last month's average of roughly 110 attacks a day was the most in a June since the war began, according to coalition statistics released on Thursday. June had more "enemy-initiated attacks"—insurgent gunfire and...