A Saudi-led military coalition said Saturday it made mistakes in an airstrike last month that killed dozens of Yemeni schoolchildren, a rare admission of guilt for the U.S.-backed alliance.

The coalition, which is fighting a war against Yemen’s Iran-supported Houthi rebels, apologized for the strike and promised to hold accountable those responsible, pending the official findings from a Saudi-based investigatory body, according to a statement.

The...