Lindsey Graham, a senior US Republican senator, has said his campaign email account was hacked by Russians.
Sen Graham also told CNN he believed "the Russians hacked into" the Democratic National Committee.
And he accused Russia of trying to "destabilise democracy all over the world", calling for a tough response.
President-elect Donald Trump earlier rejected a CIA assessment that Russian hackers tried to sway the 8 November election in his favour.
In a separate development, NBC News reported that US intelligence officials now believe with "a high level of confidence" that Russian President Vladimir Putin became personally involved in a covert Russian campaign to interfere in the US presidential election.
Russian officials have repeatedly denied the hacking accusations.
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Sen Graham, a member of the powerful Senate Armed Services Committee, told CNN that "we were told by the FBI in August that we were hacked in June".
He also said that he believed that "all the information released publicly hurt Clinton and didn't hurt Trump."
But he stressed that the outcome of the election was not in doubt.
"I think Hillary Clinton lost because she wasn't an agent of change and she tried to disqualify Trump and she wasn't able to do it."
However, Sen Graham added that this was not "a Republican or Democratic issue" and must be tackled on a bipartisan basis.
He accused Russia of attempting to destabilise democracy.
"We should tell the Russians that on no uncertain terms, you interfere in our elections, we don't care why, we're going to hit you and hit you hard, we're going to introduce sanctions."