WASHINGTON—Over just two days this week, the Trump administration has both suedAT&T Inc. to block its planned takeover of Time Warner Inc. and proposed allowing internet-service providers—like AT&T—to form closer alliances with content companies, like Time Warner.

The two government moves seem to go in opposite directions, on the one hand restricting a major telecommunications merger and on the other giving internet providers broad new powers to shape their customers’ online experiences.

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