President Trump on Friday defended his new lawyer, Rudolph W. Giuliani, who ignited a media firestorm when he revealed the Mr. Trump reimbursed a $130,000 hush-money payment to porn star Stormy Daniels.

“He’s a great guy,” the president told reporters as he left the White House en route to an NRA convention in Dallas.

Mr. Trump said that Mr. Giuliani’s chief qualification to handle his legal defense against special counsel Robert Mueller’s Russia probe is that he knows it is a “witch hunt.”

“That’s what he knows. He’s seen a lot of them, and he said he’s never seen anything so horrible,” he said of Mr. Giuliani, a former New York City mayor and presidential candidate who has long been close to Mr. Trump.

“Rudy knows it’s a witch hunt. He started yesterday. He’ll get his facts straight,” Mr. Trump said. “What he does feel is it is a very bad thing for our country, and he happens to be right.”

The president said his treatment by the special counsel contrasted sharply with the treatment of his Democratic rival Hillary Clinton, who was cleared of using a secret email server and mishandling classified material as secretary of state.

“As an example, 33,000 [of Mrs. Clinton’s] emails requested by Congress with a subpoena, and they get burned, they get deleted, and nobody says anything,” the president said. “Give me a break.”

In a blitz of TV interviews that began Wednesday night, Mr. Giuliani revealed Mr. Trump repaid his personal lawyer, Michael Cohen, for a $130,000 payment to Ms. Daniels days before the 2016 presidential election.

Mr. Cohen is now the target of an FBI investigation. His office, home and hotel room were raided last month.

The payment to Ms. Daniels, whose real name is Stephanie Clifford, was part of a nondisclosure agreement regarding her alleged sexual relationship with Mr. Trump in 2006.

Mr. Trump last month said he did not know about the payment to Ms. Daniels.

Mr. Giuliani said the president reimbursed Mr. Cohen with routine monthly retainer payments and didn’t learn until later about the nondisclosure agreement.

The disclosure and other comments by Mr. Giuliani triggered an onslaught of reports accusing Mr. Trump of lying to the American people and potentially being exposed to charges for campaign finance violations or criminal charges such as bank fraud.