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WASHINGTON, DC - JULY 09:  U.S. Circuit Judge Brett M. Kavanaugh looks on as U.S. President Donald Trump introduces him as his nominee to the United States Supreme Court during an event in the East Room of the White House July 9, 2018 in Washington, DC. Pending confirmation by the U.S. Senate, Judge Kavanaugh would succeed Associate Justice Anthony Kennedy, 81, who is retiring after 30 years of service on the high court.  (Photo by Chip Somodevilla/Getty Images)
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WASHINGTON, DC - JULY 09: U.S. Circuit Judge Brett M. Kavanaugh looks on as U.S. President Donald Trump introduces him as his nominee to the United States Supreme Court during an event in the East Room of the White House July 9, 2018 in Washington, DC. Pending confirmation by the U.S. Senate, Judge Kavanaugh would succeed Associate Justice Anthony Kennedy, 81, who is retiring after 30 years of service on the high court. (Photo by Chip Somodevilla/Getty Images)
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(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.

“Thank you. And it would have been great if you could have said that last night. Thank you,” she said.

Earlier Thursday, Kavanaugh testified that he hasn’t had any “inappropriate” conversations about the special counsel’s Russia investigation “with anyone,” adding he doesn’t “recall any conversations of that kind with anyone” at Kasowitz Benson Torres.

“I don’t recall any conversations of that kind with anyone at that law firm,” Kavanaugh said. “I haven’t had any inappropriate conversations about that investigation with anyone.”

The law firm also issued a statement to CNN, saying there have been no discussions between anyone there and Kavanaugh about Mueller.

“There have been no discussions regarding Robert Mueller’s investigation between Judge Kavanaugh and anyone at our firm,” the law firm said.

Speaking to reporters, Harris had pushed back against the law firm’s statement denying any conversations were had with Kavanaugh.

“They’re not under oath,” she told CNN.

Asked if she didn’t believe them, Harris said again, “They’re not under oath. The question was asked under oath.”

Currently a judge on the US Court of Appeals for the DC circuit, Kavanaugh, 53, was nominated to the Supreme Court by Trump in July to replaced retired Justice Anthony Kennedy. If Kavanaugh is confirmed, he could establish a conservative majority on the nation’s highest court for decades.

CNN’s David Shortell, Manu Raju and Veronica Stracqualursi contributed to this report.