WASHINGTON — For months, Republican officials have complained privately that President Trump lacks the ability to confront moments of crisis with moral clarity, choosing to inflame the divisions that have torn the country apart rather than try to bring it together.

It took the importuning of his Jewish daughter and son-in-law to craft a powerful statement of outrage at anti-Semitism after Saturday’s slaughter at a Pittsburgh synagogue. Then Mr. Trump went back into partisan mode, assailing his enemies. By the evening’s end he was tweeting about baseball, and on Sunday he went after another foe.

Mr. Trump’s mixed messages after the synagogue killings and the wave of bombs sent by one of his supporters to leading Democrats have thrust his leadership into the center of the national debate with about a week until fiercely contested congressional elections. Even some supporters call him tone-deaf, and critics say his fire-and-fury style has fueled a toxic moment in American history, while defenders bristle at what they consider opportunistic attacks by opponents interested only in tearing him down.

The deaths of 11 worshipers in Pittsburgh revived questions about what signals Mr. Trump has sent, intentionally or not, to the most radical fringe elements of society. As the president notes, members of his family are Jewish and he has been perhaps the staunchest supporter of Israel to sit in the Oval Office. Yet his castigation of “globalists,” seen by some as code for Jews, and his attacks on George Soros, the billionaire financier of liberal causes, have unsettled Jewish leaders.