The Federal Trade Commission’s Democratic commissioners are pressing for more aggressive scrutiny of mergers involving non-direct competitors.

Rohit Chopra and Rebecca Slaughter, the two Democrats in the Republican-controlled panel, are joining competition advocates and lawmakers who are increasingly skeptical of “vertical” mergers, in which a company buys another in its supply chain. Their calls for changes come as the agency considers updating some of its decades-old antitrust approaches that critics say have been too lenient toward deals.

As minority members in the five-member commission, Chopra and Slaughter are, without Republican support, largely powerless to dramatically change the course of the...