After his interview, Mr. Giuliani met with Mr. Trump at his golf club in Northern Virginia.

Mr. Giuliani told the ABC anchor, George Stephanopoulos, that he was still getting up to speed on Mr. Trump’s legal issues — a fact that became apparent as the interview went on. As was the case during his interviews last week, Mr. Giuliani seemed to speak largely off the cuff. He speculated freely and contradicted himself, sometimes from one statement to the next.

He said, for example, that Mr. Mueller would be to blame if Mr. Trump refused to testify because his office had leaked a list of questions that the special counsel would like to ask him. But then he admitted he did not know who leaked the questions, which were reported by The New York Times.

Mr. Giuliani referred repeatedly to a federal judge’s criticism of the special counsel’s fraud case against Paul Manafort, the former chairman of the Trump campaign. The judge, T.S. Ellis III, said on Friday that the case seemed motivated by a desire to get Mr. Manafort to potentially incriminate Mr. Trump.

“There’s no question that the amount of government misconduct is accumulating,” Mr. Giuliani said. “Very embarrassing to my former Justice Department.”

Mr. Giuliani created a furor on Wednesday when he contradicted the president about the payment to Ms. Clifford. Speaking on Fox News, Mr. Giuliani said Mr. Trump reimbursed Mr. Cohen for a $130,000 payment that Mr. Cohen has said he made to Ms. Clifford, to keep her from making public a story about an affair she claims she had with Mr. Trump — a claim that he denies. When asked in April by reporters traveling on Air Force One whether he knew about the payment, Mr. Trump said he did not.

On Sunday, Mr. Giuliani said he was still trying to establish when Mr. Trump learned that Mr. Cohen had paid Ms. Clifford, whose stage name is Stormy Daniels. But he added that as a legal matter, it did not matter since the payment did not violate federal campaign finance rules.

Asked about the discrepancies between his account and the president’s statement, Mr. Giuliani said: “Those don’t amount to anything — what is said to the press. That’s political.”