OSAKA, Japan — They were having a good time. Like old friends reuniting, they warmly shook hands, smiled and chatted amiably. And then President Trump brushed off Russia’s interference in American democracy with a joke as President Vladimir V. Putin chuckled.

The first encounter between Mr. Trump and Mr. Putin since the special counsel Robert S. Mueller III reported that Russia conducted a “sweeping and systematic” operation to sway the 2016 election proved more convivial than confrontational. Rather than challenge Mr. Putin, Mr. Trump treated it as a laughing matter.

In the process, he triggered a fresh furor over his accommodating approach to Russia and brought back old questions that have haunted him since he took office. Angry at perceived challenges to his legitimacy, he has long dismissed or at most grudgingly accepted the conclusions of American intelligence agencies that Russia sought to help his campaign.

But while Mr. Trump once hoped to leave the investigation behind and finally recalibrate the Russian-American relationship, he instead put the issue back in the spotlight as House Democrats prepare to question Mr. Mueller on camera next month.