That message resonates with many of Ms. Gabbard’s supporters. In a moment marked by fractured politics, Ms. Gabbard’s nontraditional positions are a major part of her appeal for voters seeking to break out of polarized partisan divisions. Joe Rogan, the popular podcast host, said he planned to vote for her. Jack Dorsey, the chief executive of Twitter, donated to her campaign.

But it’s also an argument that reminds some Democrats of the narrative pushed by Russian actors during the 2016 presidential contest, when an operation by internet trolls worked to manipulate American public opinion: that the electoral system is broken and cannot be trusted.

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Some of those who have worked with Ms. Gabbard say that, as an Iraq war veteran whose chief message is that America should stop trying to police the world, she is representing viewpoints that draw support from an array of people in the United States as well as abroad .

“In reality, Tulsi is really running on an antiwar message that’s consistent with where a lot of veterans are,” said Jon Soltz, chairman of the liberal veterans organization VoteVets.org, which worked closely with Ms. Gabbard during her first congressional campaign. “I know everyone thinks there’s a conspiracy theory here but that’s really what she’s doing.”

Still, Democrats are on high alert about foreign interference in the next election and the D.N.C. is well aware of the frequent mentions of Ms. Gabbard in the Russian state news media.

An independent analysis of the Russian news media found that RT, the Kremlin-backed news agency, mentioned Ms. Gabbard frequently for a candidate polling in single digits, according to data collected by the Alliance for Securing Democracy, a group that seeks to track and expose efforts by authoritarian regimes to undermine democratic elections.