"Lawyer's liability if he made a mistake, not me", the president added, accusing Cohen - his former right-hand man - of "trying to get his sentence reduced".
In a tweet, Mr Ayers confirmed his exit from the White House.
Following Ayers' announcement, Trump said on Twitter he is "in the process of interviewing some really great people" for the position and that he will soon make a decision regarding his new chief of staff.
U.S. Trade Representative Robert Lighthizer on Sunday saying he was happy in his current role and had not been approached about the position.
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If Liverpool beat Napoli by two clear goals, they will leapfrog the Italians by virtue of head to head record and make it through. Asked about PSG's chances of winning the Champions League , Mbappe added: "We need to see what we'll have in front of us".
"It remains to be seen which direction Trump will go, but other contenders for the chief of staff position reportedly include Citizens United president Dave Bossie-who served as deputy campaign manager for Trump in 2016-and US trade representative Robert Lighthizer, as well as Blackstone lobbyist Wayne Berman".
Trump has told confidants that he wants his third chief of staff to be someone he can chat with - trading gossip and complaining about media coverage - as well as someone more attuned politically.
Conway's husband, George, who has frequently spoken out about Trump saw it differently in his response to a tweet from Dartmouth University administrator Daniel Benjamin.
There is no doubt that managing the White House under Trump would be a chaotic job. The position of chief of staff doesn't require Senate approval, so the decision is fully up to the president.
And it remains unclear who wants the job. And of course the worst-case scenario is you become H.R. Haldeman, who went to jail for 18 months after participating in Richard Nixon's cover-ups. He will be working on the fundraising efforts for Trump's reelection.
The president does operate in this highly personalistic style and what we're hearing about Kelly's frustrations are identical to the frustrations that we're hearing from a number of other people who've left the administration like Rex Tillerson, who clashed with the president just in the past week over what it had been like for them to work together.
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Quatrième du classement du Ballon d'Or 2018 et vainqueur du premier trophée Kopa, Kylian Mbappé étonne de jour en jour par sa précocité.
Even the best counsel will matter little unless Mr Trump trusts his new chief of staff and will listen to frank advice, Mr Panetta said.
According to Collins, he simply said his credentials are ready.
But critics questioned whether the young operative had the kind of experience needed to deal with the internal strife that has often engulfed the Trump White House.
HORSLEY: Once upon a time, Trump himself seemed to acknowledge that.
On MSNBC on Monday, Ron Klain, chief of staff for Vice Presidents Al Gore and Joe Biden, also described the couple as "floating powers behind the scenes" who work outside any chain of normal of accountability.
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If we do see further contractions to U.S. stockpiles, there is a strong chance that we will see crude start to gain ground. It fell quite hard yesterday, so it might correct higher", PVM Oil Associates Tamas Varga said.