Nadler did not get into the specifics of what Whitaker said when he met with Nadler and the top Republican on the panel, Georgia Rep. Doug Collins.
At the the hearing last month, Whitaker gave what appeared to be a carefully phrased statement meant to exonerate the president from allegations that could lead to charges he tried to subvert the investigation into Cohen, Trump's former lawyer.
The campaign finance case in NY mentioned by Nadler involves hush money payments made to adult film actress Stephanie Clifford, known as Stormy Daniels, and former Playboy model Karen McDougal, just before the 2016 election.
Whitaker also told Nadler and Collins Wednesday that he had discussions with his staff about firing certain federally appointed district attorneys.
Two, while he was acting attorney general, Mr. Whitaker was directly involved in conversations about whether to fire one or more US attorneys.
Collins, however, said that the conversations were part of normal personnel decisions while Whitaker was atop the Justice Department, and there was nothing "nefarious" about those talks.
Giuliani had previously said he never offered anyone a pardon on the president's behalf.
The meeting Wednesday with Whitaker was private.
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"The FM assured me that Pakistan would deal firmly with all terrorists and will continue steps to de-escalate tensions with India", he said.
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News reports said Trump did lash out at Whitaker, but Whitaker said in the hearing that he did not.
Nadler said Whitaker's response about the Cohen case came after he was pressed in the closed-door session about CNN reporting in December that Trump twice vented to Whitaker about federal prosecutors who referenced the President's actions in crimes Cohen pleaded guilty to.
"He would not say no", Nadler said when pressed further. Committee Republicans had no say in determining ground rules for the second meeting.
At the February hearing, which was held while Whitaker was still acting attorney general, Democrats confronted him on his past criticism of special counsel Robert Mueller's work and his refusal to recuse himself from overseeing it, attacked him over his prior business dealings and challenged his credentials as the country's chief law enforcement officer.
Cohen's public committee testimony last month "could have been clearer and more complete", Monico wrote in the letter obtained by The Associated Press.
Cohen is slated to begin a three-year prison sentence in May.