At a Senate hearing soon after President Trump’s first election eight years ago, Marco Rubio had a simple question for the next U.S. secretary of state: “Is Vladimir Putin a war criminal?”

Mr. Rubio, then a Florida senator, posed the question to the Texas oilman Rex Tillerson at his confirmation hearing in January 2017. He would have known well that he was putting Mr. Tillerson in an awkward position. Mr. Trump was an open admirer of Mr. Putin, despite the Russian leader’s pariah status in the West and — against the advice of Mr. Rubio and many others in Congress — hoped to restore fractured relations between Washington and Moscow.

Mr. Tillerson dodged the question, saying he needed to study the evidence before drawing conclusions. Mr. Rubio tried again, this time ticking off atrocities committed by Russia’s military and the many suspicious murders of Mr. Putin’s critics. Mr. Tillerson again deflected.

The exchange left Mr. Rubio visibly frustrated. “I find it discouraging, your inability to cite that which I think is globally accepted,” Mr. Rubio said.

Secretary of state is “the second most important position in the U.S. government, with all due respect to the vice president,” because of its global influence, he later told Mr. Tillerson. It was critical, he added, that the job’s occupant speak with “moral clarity.”