While senior Trump administration officials said this week that Iran has been actively interfering in the presidential election, many intelligence officials said they remained far more concerned about Russia, which in recent days has hacked into state and local computer networks in breaches that could allow Moscow broader access to American voting infrastructure.

The discovery of the breaches came as American intelligence agencies, infiltrating Russian networks themselves, have pieced together details of what they believe are Russia’s plans to interfere in the presidential race in its final days or immediately after the election on Nov. 3. Officials did not make clear what Russia planned to do, but they said its operations would be intended to help President Trump, potentially by exacerbating disputes around the results, especially if the race is too close to call.

F.B.I. and Homeland Security officials also announced on Thursday that Russia’s state hackers had targeted dozens of state and local governments and aviation networks starting in September. They stole data from the computer servers of at least two unidentified targets and continued to crawl through some of the affected networks, the agencies said. Other officials said that the targets included some voting-related systems, and that they may have been collateral damage in the attacks.

So far, there is no evidence that the Russians have changed any vote tallies or voter registration information, officials said. They added that the Russian-backed hackers had penetrated the computer networks without taking further action, as they did in 2016.

But American officials expect that if the presidential race is not called on election night, Russian groups could use their knowledge of the local computer systems to deface websites, release nonpublic information or take similar steps that could sow chaos and doubts about the integrity of the results, according to officials briefed on the intelligence. Such steps could fuel Mr. Trump’s unsubstantiated claims that the vote is “rigged” and that he can be defeated only if his opponents cheat.