U.S. allies Canada, Japan and the European Union are banding together to increase pressure on Washington following the Trump administration’s metals tariffs as they head to a meeting of Group of Seven industrialized countries in Quebec on Friday.

With trade likely to dominate the agenda of the summit, the U.S. tariff move has driven a wedge between the U.S. and the other six nations, say leaders and officials, and has dashed hopes that the group would focus on a coordinated response to another longstanding trade issue: the...