But the diplomatic theater playing out in Moscow on a rainy Wednesday morning was far from boring: Mr. Putin, operating on home turf, was looking for any way to shape the narrative of Mr. Tillerson’s first trip here as secretary of state.

The outcome could well decide whether Mr. Trump’s oft-stated desire to remake American relations with Moscow will now disintegrate, just as similar efforts by Barack Obama did early in his presidency.

Russia said earlier this week that Mr. Putin would not meet with Mr. Tillerson, but on Wednesday the Russian leader’s spokesman, Dmitri S. Peskov, held out the possibility of a meeting later in the day. Russian leaders have greeted virtually all new secretaries of state since the end of World War II, but Mr. Peskov said any meeting would depend on how Mr. Tillerson’s other talks went.

The drama appeared to be an effort by Mr. Putin to show that he was in control.

Critics of the Trump administration insist that the series of events around the attack in Syria had been meant to distract from the investigation into possible ties between the Trump campaign and Russia.

Mr. Tillerson, who was recognized with an Order of Friendship medal by the Russian government while he was the chief executive of Exxon Mobil, has insisted on a tough line on Russia, ruling out any early end to sanctions unless the country returns Crimea to Ukraine and ceases meddling elsewhere.

On Syria, Mr. Tillerson delivered what sounded much like an ultimatum to the Russians on Tuesday while talking to reporters at a Group of 7 meeting in Italy.

“I think it is clear to all of us that the reign of the Assad family is coming to an end,” Mr. Tillerson said, echoing a theme first heard from Mr. Obama in 2011, when the Arab Spring led many to believe the Syrian leader was about to be overthrown.