Asked at a press conference if he plans to resign, Sessions replied: "I have the honor of serving as attorney general. It is something that goes beyond any thought I would have ever had for myself."
"I plan to continue to do so as long as that is appropriate," he added, speaking to reporters at a press conference about the shutdown of two "dark web" marketplaces.
In an interview with The New York Times on Wednesday, Trump said he would never have chosen Sessions for the post if he had known the former senator would recuse himself.
"How do you take a job and then recuse yourself? If he would have recused himself before the job, I would have said, 'Thanks, Jeff, but I'm not going to take you,'" Trump said.
The US president also criticized Sessions's testimony during his Senate confirmation hearing, when he denied "communications with the Russians" despite at least two meetings with Russian Ambassador Sergey Kislyak during the campaign.
"Jeff Sessions gave some bad answers," the president told the Times.
"He gave some answers that were simple questions and should have been simple answers, but they weren't."
When asked how he could continue to work without the confidence of Trump, Sessions replied: "We are serving right now. The work we are doing today is the kind of work we intend to continue."
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