When WikiLeaks and other websites published troves of hacked emails from the Democratic National Committee and Hillary Clinton’s campaign during the final months of the presidential election, the American news media enthusiastically seized on the documents to illuminate the inner workings of a political party and its standard-bearer.

But as more information emerges about the extent of Russia’s involvement in the hacking, news organizations are reassessing the journalistic challenges involved in relying on stolen documents. While the Obama administration had said in the weeks before the election that the Kremlin had directed the attacks, intelligence agencies now believe that Russia may have interfered in the campaign with the goal of promoting the candidacy of Donald J. Trump.

In a deeply reported story on the Russian cyberattacks, The New York Times wrote this week that news organizations, including The Times, had become “a de facto instrument of Russian intelligence” by basing so many stories on the hacked emails. It was an unusually blunt assessment of the role news organizations played in disseminating stolen information that may have shaped public opinion heading into the election.

Many top editors say that stolen documents that are deemed newsworthy are fair game for coverage, but that the potential motives behind the release of the material must be made clear to readers. Though a mountain of hacked Democratic Party emails was made available, they said, they published articles only on those judged to be in the public interest, with appropriate context provided, given the information available at the time.