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(CNN) —  

Former New York City Mayor Rudy Giuliani on Monday swatted away a report that he is a contender to replace Attorney General Jeff Sessions, and said Sessions made the right decision to recuse himself from the Russia investigation.

Giuliani said there is no truth to a report by Axios that said Trump has recently raised the possibility of tapping Giuliani to replace Sessions, whom the President referred to as “beleaguered” on Monday, days after publicly rebuking Sessions for recusing himself from the federal investigation into Russian election meddling in the 2016 campaign.

Sessions “made the right decision under the rules of the Justice Department” in recusing himself from the investigation, Giuliani told CNN on Monday after landing at Ronald Reagan Washington National Airport.

Speculation about Sessions’ future has run rampant since Trump last week expressed remorse about tapping Sessions, one of his earliest supporters in Washington, to lead the Justice Department.

“Sessions should have never recused himself, and if he was going to recuse himself, he should have told me before he took the job and I would have picked somebody else,” Trump told the New York Times last week.

Facing a wave of pressure from Democrats and Republicans alike, Sessions announced his recusal in March without consulting the President. But Trump’s anger over the recusal only grew in subsequent months after the deputy attorney general, charged with oversight over Russia matters in the wake of Sessions’ recusal, appointed a special counsel to lead the investigation into contacts between Trump’s campaign and Moscow.

In a news conference the day after the Times interview, Sessions offered no indication he plans to resign. He also sent no signals that he might resign after The Washington Post on Friday reported on Russian intelligence intercepts in which then-Russian Ambassador to the US Sergey Kislyak claimed he discussed campaign matters with Sessions during the campaign – despite Sessions’ previous claims to the contrary.

Trump and Sessions have not talked since – at least – the Times interview, according to two White House officials.

But Sessions was at the White House on Monday for meetings, including one with White House counsel Don McGahn, newly-minted White House communications director Anthony Scaramucci said.

Scaramucci declined to say whether the President wants Sessions to resign.

“They need to sit down face to face and have a reconciliation and a discussion of the future,” he said. “They need to speak and determine what the future of the relationship looks like.”

Trump continues to be angry with Sessions, according to one aide and hasn’t yet requested a meeting with Sessions.

Trump’s advisers have also explained to him – amid his fury about Sessions – that anyone who was part of his campaign, including Giuliani, would likely face pressure to recuse themselves from the Russia investigation, according to Trump advisers and officials.

CNN’s Kaitlan Collins and Jeff Zeleny contributed to this report.