MI5 chief Sir Ken McCallum has said there was Russian interference in the the Brexit referendum, but warned against overstating its impact on the result.
It comes after Prime Minister Andy Burnham provoked a backlash from some Brexit campaigners by saying it was "clear" there had been interference by Moscow in the 2016 vote.
Sir Ken said it was "a matter of public record" that there was interference in the referendum by online trolls and bots.
However, he suggested Russian trolls would be "delighted" to be front page news again, "despite the comparative unimpressiveness" of their efforts.
He added: "There is a really important difference between interference attempted and outcome swayed.
"I am a little bit anxious that we don't play into our adversaries' hands by making these trolls look 10ft tall."
Conservative deputy leader Alex Burghart branded Sir Ken's comments "an extraordinary slap down to the prime minister".
In an interview released on Monday, Burnham told The Rest is Politics podcast, external that upon arriving in Downing Street, he had asked if there had been Russian interference in the 2016 vote, adding: "I've had the clear answer that, yes, there was."
He did not provide details about the extent or nature of Russian activities during the interview, and when pressed on the subject in the House of Commons on Monday afternoon appeared to be less definitive.
The PM denied claims from Conservative leader Kemi Badenoch that he was implying the referendum result was illegitimate because of Russian interference.
He said it was a "matter of record" that Russia sought to interfere in the 2019 general election, adding: "We think it is inconceivable that this was the first time".
A No 10 spokesperson also clarified that while the prime minister believed it was highly likely Russia tried to influence the referendum result, he did not believe those efforts were successful.
The Conservatives accused Burnham of making an "embarrassing retreat" after "being caught out trying question the legitimacy of the referendum result".
Answering questions after his annual speech at MI5's London headquarters earlier, Sir Ken said: "It is openly on the record that Russia Today and Sputnik and other Russian media organisations came in pretty strongly around the referendum.
"And it is also a matter of open source record that there was a certain amount of interference attempted through trolls and bots and so forth."
He added that he agreed "strongly" with the PM that there was a hack and leak during the 2019 general election campaign.
However, he raised concerns about the impact of the debate on Russian interference.
"It is kind of up to us how far we allow our various adversaries to divide us," Sir Ken said.
"And I'm a little bit worried that if we all stay in this debate for another few days, that Russian trolls who didn't appear to do all that much at various points over the years, they'll be delighted because they are front page news again despite the comparative unimpressiveness of what they do at all points along the journey."
Reform UK leader Nigel Farage has accused Burnham of lying, saying there was "no Russian interference" in the referendum.
Meanwhile, former Prime Minister Boris Johnson said that in 2016, when he became foreign secretary, the security services had told him "there was no evidence of any successful interference in the 2016 referendum, by Russia or any other power".
He added: "Either the security services have changed their view - which would be very odd - or Burnham is lying about what he has been told."
In 2020, a parliamentary report did not reach a firm conclusion on whether Russia had tried to intervene in UK elections and referendums, but criticised the government for failing to fully assess and counter the threat from Russian "troll" accounts on social media.