Opposition is steadily growing to AT&T Inc.'s proposed $39 billion takeover of T-Mobile USA, as competitors, state regulators and elected officials have come out in recent days expressing concerns about the acquisition from Deutsche Telekom AG.

The views add to pressure on a combination—of the second- and fourth-largest wireless carriers in the U.S.—that has already raised serious initial concerns at the Justice Department, which is worried it will hurt competition, according to people familiar with the matter.

The...