Washington (CNN) Supreme Court nominee Brett Kavanaugh said definitively Thursday that he has not had a conversation with anyone at Kasowitz Benson Torres, the law firm founded by President Donald Trump's personal attorney, about special counsel Robert Mueller's investigation of Russian interference in the 2016 election.

"The answer is no," Kavanaugh said at the end of another tense exchange with Democratic Sen. Kamala Harris of California.

Harris, often mentioned as a possible 2020 presidential candidate, had pressed Kavanaugh on Wednesday , and the nominee had said he was unsure. Thursday, Harris noted that the exchange had generated headlines and said she had "reliable information" that there had been a conversation.

"I'm sure you've noticed your lack of a clear answer to a question I asked you last night has generated a lot of interest," Harris told Kavanaugh on Thursday. "I received reliable information that you had a conversation about the special counsel or his investigation with the law firm that has represented President Trump."

Harris did not offer any proof to back up her assertion and moved on to other topics.

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