NEW YORK -- President Donald Trump is growing increasingly irritated with lawyer Rudy Giuliani's frequently off-message media blitz, in which he has muddied the waters on hush money paid to porn actress Stormy Daniels and made claims that could complicate the president's standing in the special counsel's Russia probe.

Trump has begun questioning whether Giuliani, the former New York City mayor, should be sidelined from television interviews, according to two people familiar with the president's thinking but not authorized to speak publicly about private discussions.

Trump also expressed annoyance that Giuliani's theatrics have breathed new life into the Daniels story and extended its lifespan. It's a concern shared by Trump allies who think Giuliani is only generating more legal and political trouble for the White House.

Giuliani, the newest addition to the president's legal team, first rattled the White House last week when he sat for interviews on Fox News and seemed to contradict Trump's previous statements by saying the president was aware of the October 2016 payout to Daniels from his personal attorney, Michael Cohen. He also suggested the settlement with Daniels had been made because Trump was in the stretch run of his presidential campaign.

After Trump chided Giuliani on Friday, saying the lawyer needed to "get his facts straight," the former mayor put out a statement trying to clarify his remarks. But in weekend interviews, Giuliani appeared to dig himself a deeper hole by acknowledging that "Cohen takes care of situations like this, then gets paid for them sometimes." He did not rule out the possibility that Cohen had paid off other women.

Trump, who has denied the affair with Daniels, was angry that Giuliani had given the impression that other women may make similar charges of infidelity, according to the people familiar with his views.

Additionally, Trump has grown agitated in recent days by cable news replays of Giuliani's Wednesday interview with Sean Hannity, in which he first said that Trump knew about the payment but claimed it wouldn't be a campaign violation. A clearly surprised Hannity then asked, "Because they funneled it through the law firm?"

To which Giuliani responded, "Funneled it through the law firm, and the president repaid him."

Trump snapped at both men in recent days, chiding Hannity for using the word "funneled," which he believes had illegal connotations, according to the people. As for Giuliani, the president has not yet signalled to him to stop appearing on television, but told a confidant recently that perhaps his new lawyer should "be benched" at least temporarily, if he can't improve his performance.

The president has not publicly discussed dismissing Giuliani and has been appreciative of his sharp attacks on the Russia investigation and his forceful battles with the press, according to three White House aides and outside allies. The two men have spoken frequently, according to officials familiar with their interactions.

But many Trump allies both inside and outside the White House have grown anxious in recent days about Giuliani's whirlwind and unpredictable interviews.

"They're admitting to enough that warrants scrutiny. It shouldn't be put on television shows off the cuff," said Alan Dershowitz, the emeritus Harvard law professor who has been informally advising Trump on the Russia collusion probe. "This is not the way to handle a complicated case."

Trump, according to one confidant, celebrated Giuliani's hiring last month by declaring that he had enlisted "America's F---ing Mayor" as a legal attack dog with star power. But many in the White House have begun evoking comparisons with Anthony Scaramucci -- who, like Giuliani, was a hard-charging New Yorker with a knack for getting TV airtime.

Scaramucci only lasted 11 days before being fired. The former White House communications director himself drew parallels between his own burn-bright-burn-fast tenure and Giuliani's performance -- but said he meant it as a "big compliment."

"I am enjoying all of the comparisons between me and the mayor .RudyGiuliani," Scaramucci tweeted Sunday. "He is loyal, tough and a fierce competitor. He fights and will win for ΓåòrealDonaldTrump ΓåòPOTUS. Big compliment thank you!"

Giuliani did not respond to requests for comment.

West Wing aides were blindsided by Giuliani's TV appearances last week and many senior advisers and members of the president's legal team have been cut out of the decision-making process. But some aides have been reluctant to broach the subject with Trump because it only increases their liability, according to officials.

Press Secretary Sarah Huckabee Sanders, who was among those surprised by Giuliani's string of TV appearances, said Monday that Trump felt the former mayor "added value" to his outside legal team. On Friday, Trump said Giuliani was "a great guy but he just started a day ago" on the defence team. He made clear the former New York mayor was still "learning the subject matter."

Some West Wing aides have complained that Giuliani, who ran for president in 2008, was acting like a "principal" and not a member of a team. And some in Trump's inner circle raised their eyebrows at Giuliani's declaration that Jared Kushner, the president's son-in-law and senior adviser, was "disposable." He also declined to rule out Trump invoking the Fifth Amendment in special counsel Robert Mueller's ongoing Russia probe.

Trump has repeatedly railed against those who take the Fifth, declaring at one September 2016 campaign rally: "The mob takes the Fifth. If you're innocent, why are you taking the Fifth Amendment?"

The episode revived worries in Trump's inner circle about Giuliani, who enjoys the media limelight and has a tendency to go off-script. His behaviour grew more unpredictable during the stretch run of the 2016 presidential campaign, when Trump chided him for falling asleep on the campaign plane, according to two former campaign officials.

Giuliani also alienated a number of people in Trump's inner circle by insisting that the only Cabinet position he would consider would be secretary of state. He did not get the post.

Giuliani's remarks have also been watched with concern at the State Department and Pentagon after he weighed in recently on international affairs, raising questions about whether he was speaking for the president. He declared last week that North Korea would be releasing three Americans being held captive, which has not yet happened, and said the administration was committed to regime change in Iran, a stance Trump has not taken.

"He speaks for himself and not on behalf of the administration on foreign policy," State Department spokeswoman Heather Nauert said Monday.

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Associated Press writers Zeke Miller and Josh Lederman contributed reporting from Washington.