"Well, I don't think I am doing that. But I am disappointed in the attorney general," Trump told reporters yesterday when asked whether he would be firing Sessions after he went against him on twitter.
Trump was addressing a news conference at the White House with visiting Lebanese Prime Minister Saad Hariri.
Earlier in the day, Trump accused Sessions of being "very weak" in the investigation into former secretary of state and the 2016 Democratic presidential candidate Hillary Clinton's emails.
Over the last few days, Trump had gone public in expressing dissatisfaction over Sessions' position on investigations related to Russian interference in the American presidential elections last year.
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Sessions has recused himself from the government's probe of Russian meddling in the US election.
"He (Sessions) should not have recused himself almost immediately after he took office. If he was going to recuse himself, he should've told me prior to taking office and I would've, quite simply, picked somebody else," the president told the news conference.
"I think it's unfair to the presidency. And that's the way I feel," he said.
The attorney general has said that he would stay in the position as long as it is appropriate.
Responding to another question, Trump said he wants Sessions to be much tougher when it comes to leaks of classified material.
"I want the attorney general to be much tougher on the leaks from intelligence agencies, which are leaking like rarely have they ever leaked before, at a very important level. These are intelligence agencies. We cannot have that happen," he said.