President Trump said Friday that Rudy Giuliani, his new lawyer who claimed Mr. Trump repaid Michael Cohen for the $130,000 payment to adult film star Stormy Daniels, only joined his legal team Thursday and will "get his facts straight."

Mr. Trump made the comments to reporters Friday on his way to address the National Rifle Association in Dallas. Trump on Friday did not specify what among Giuliani's claims was perhaps incorrect, offering vague comments like, "Learn before you speak."

"Rudy knows it's a witch hunt," Mr. Trump said. "He started yesterday. He'll get his facts straight. He's a great guy."

Get Breaking News Delivered to Your Inbox

Asked when Mr. Trump learned what he knows now about Cohen's payment to Daniels and any subsequent events, Mr. Trump said, "You're going to find out, because we're going to give a full list."

Then, after he arrived at Andrews Air Force Base, the president talked to the press again, telling them that Giuliani "wasn't totally familiar with everything."

"I will tell you this, when Rudy made the statement, Rudy is great but Rudy had just started and wasn't totally familiar with everything," Mr. Trump said. "And Rudy, we love Rudy, he's a special guy but what he understands is that this is a witch hunt. He probably understands that better than anybody."

But Mr. Trump had already seemed to confirm Giuliani's claims on Sean Hannity's Fox News show "Hannity" Wednesday night in tweets of his own Thursday morning.

"Mr. Cohen, an attorney, received a monthly retainer, not from the campaign and having nothing to do with the campaign, from which he entered into, through reimbursement, a private contract between two parties, known as a non-disclosure agreement, or NDA," Mr. Trump tweeted at the time.

Friday marked the first time Mr. Trump fielded questions since Giuliani's appearance on Fox News — and numerous subsequent interviews. White House press secretary Sarah Sanders insisted Thursday Mr. Trump was unaware of Cohen's payment at the time, learning about it only later. Daniels alleges she had a sexual encounter with Mr. Trump in 2006, which the White House has said Mr. Trump denies.

Mr. Trump commented on another topic Friday — special counsel Robert Mueller. Mr. Trump said he would "love" to sit down with Mueller, even if it goes against the advice of his own lawyers. That's because, "nobody wants to speak more than me because we have done nothing wrong," Mr. Trump said. "No collusion! No obstruction."

"I would love to speak. Nobody wants to speak more than me," Mr. Trump said.

Mr. Trump also touted economic growth and the unemployment rate, which is 3.9 percent. Mr. Trump declared the country has reached "full employment," an economic term that means nearly all people who want to work, and are able to, are employed. Unemployment figures do not take into account underemployment, and those who have dropped out of the job hunt.