Speaking separately to Russian reporters in Hamburg, the Russian foreign minister, Sergei V. Lavrov, cast Mr. Trump in a more forgiving light.

“President Trump said that this campaign has already taken on a rather strange character, because over the many months that these accusations have been made, not a single fact has been presented,” Mr. Lavrov said. “President Trump said that he had heard the clear statements from President Putin about this being untrue, that the Russian leadership did not interfere in the election, and that he accepts these statements.”

Mr. Lavrov, a veteran diplomatic infighter, added one more detail: Mr. Trump, he said, had conceded “that certain circles in the U.S. are still exaggerating, although they cannot prove this, the topic of Russia’s interference with the U.S. election.”

An email to a spokesman for Mr. Trump wasn’t immediately returned.

As recently as Thursday, Mr. Trump – who has vehemently denied that Moscow played any role in his victory — conceded that Russia might have had some hand in trying to sway the election, but he also left open the possibility that other countries had taken similar actions.

Mr. Tillerson said that after Mr. Putin asked for evidence of Russian meddling, Mr. Trump moved on to other topics, notably Syria. Mr. Trump, he said, was more concerned with the future than the past.

American officials would continue to discuss a “framework” for an agreement with Mr. Putin to forswear such actions in the future, he added.

Mr. Tillerson was less than sanguine about the prospects of ever getting Russia to admit meddling. “It may be simply an intractable disagreement at this point,” he said.

— Glenn Thrush and Neil MacFarquhar