When asked why the disclosure about Russia’s attempted assistance came out on Friday, Mr. Sanders said: “I’ll let you guess about one day before the Nevada caucus. Why do you think it came out? It was The Washington Post? Good friends.”

The candidates are doing to one another what the Russians are trying to do to the election: weaponize the information. With Russia seemingly pulling levers from behind a curtain, they’re attempting to create a narrative about whom Mr. Putin might support or oppose.

Mr. Trump suggested at a rally in Las Vegas that Mr. Putin would prefer Mr. Sanders, claiming that Mr. Sanders and his wife had “honeymooned in Moscow.” (The couple did travel to the Soviet Union after their wedding, and have jokingly called the trip their honeymoon, but they had a more traditional honeymoon the next year in the Caribbean.)

Michael Bloomberg’s aides made a similar argument: “Trump himself and now the Russians are indicating that Senator Sanders is the candidate they want to run against,” Dan Kanninen, a campaign official, told reporters on Monday.

And Joseph R. Biden Jr., who said he had not been informed of any specific intelligence about Russia and his campaign, said he was the candidate Mr. Putin most hated.

“The Russians don’t want me to be the nominee,” he said on “Face the Nation.” “They spent a lot of money on bots on Facebook, and they’ve been taken down, saying Biden is a bad guy. They don’t want Biden running. They’re not — no one’s helping me to try to get the nomination.”

Turning disinformation into just another political football is exactly the kind of reaction Russia hopes to foster. The point of Moscow’s campaign is not necessarily to help Mr. Trump or Mr. Sanders get to the presidency in 2020; it’s to sow discord and undermine the institutions of American democracy, making presidential elections here seem no more credible than the ones keeping Mr. Putin in office.