He also suggested Donald Trump’s campaign was given advance notice of the breach.
John Podesta’s remarks come after WikiLeaks published a trove of his hacked emails.
Hillary Clinton’s top adviser said the enquiry was part of a wider probe into hacks on the Democratic Party by groups with Russian ties.
“I’ve been involved in politics for nearly five decades,” John Podesta told reporters aboard the Clinton campaign plane.
“This definitely is the first campaign that I’ve been involved with in which I’ve had to tangle with Russian intelligence agencies, who seem to be doing everything they can on behalf of our opponent.”
John Podesta pointed to a tweet by Donald Trump’s adviser Roger Stone in August that said Podesta’s “time in the barrel” was coming.
However, the tweet was posted shortly after WikiLeaks released thousands of hacked emails from other Democratic officials.
John Podesta also claimed Roger Stone has been in touch with WikiLeaks founder Julian Assange, but acknowledged evidence was “circumstantial”.
Roger Stone told the AP that John Podesta’s claims were “categorically false” while WikiLeaks tweeted that it “has had no contact with Roger Stone”.
John Podesta also speculated that the timing of the first WikiLeaks release on October 7 was intended to distract from the explosive 2005 footage showing Donald Trump making inappropriate comments about groping women.
The Clinton campaign has not verified the authenticity of the leaked emails, adding that they could have been altered.
Hillary Clinton’s spokeswoman, Jennifer Palmieri said: “The pattern is they hack, they leak truthful things, and then they build up to leaking documents that are either doctored or wholly fabricated.”
The latest batch of emails offer a glimpse into Hillary Clinton’s political network, suggesting that Donna Brazile, Democratic National Committee interim chairman, had given the nominee advance notice of a question she would be asked at a CNN town hall event.
Donna Brazile denied any impropriety on October 11.
US relations with Russia have taken a central role in the presidential election.
Last week, US intelligence officials said the Russian government was behind a series of hacks aiming to influence the presidential election.
Hillary Clinton has also questioned Donald Trump’s praise for Russian President Vladimir Putin as a strong leader, his connection to Russian businessmen and his criticism of the NATO alliance.
Russian foreign minister Sergey Lavrov told CNN the hacking allegations were flattering but ridiculous.
When asked about Donald Trump’s comments about women, Sergey Lavrov said there were “pussies” on both sides.
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