WASHINGTON—The U.S. Senate this week is set to vote on a resolution to withdraw U.S. support for the Saudi-led coalition at war in Yemen, an effort to punish Riyadh for the killing of a Saudi Arabian journalist.

The measure is just one of several lawmakers have introduced that would pit a Senate skeptical about the U.S. relationship with Saudi Arabia against the Trump administration, which views the kingdom as a vital strategic ally.

A...