"I don't have a comment on that", Spicer told reporters during his daily briefing, when asked to describe the president's confidence in Sessions.
President Donald Trump has scheduled a speech addressing religious conservatives around the same time that former Federal Bureau of Investigation director James Comey is expected to testify before Congress.
Justice Department spokeswoman Sarah Isgur Flores declined to comment.
"I have not had a discussion with him (Trump) about that", Spicer said.
But pressure has been mounting on Trump over his campaign's communications with Russians. Trump's tweets were, others agreed, a remarkably self-destructive move with no obvious strategy behind them, besides riling up his base.
Trump has decided that media inquires would best be handled by his outside lawyer in NY instead of a team inside the White House, the magazine reported late Tuesday.
Sessions has said his decision came after he consulted extensively with Justice Department lawyers about what was appropriate.
But the exchange comes amid increasingly outward signs of displeasure from Mr. Trump and the White House regarding Mr. Sessions and the Justice Department more broadly.
Trump has "lashed out" at Sessions for recusing himself, ABC News reports, as he believes the recusal has allowed for the investigation to grow and subsequently become the purview of newly appointed Special Counsel Robert Mueller. The tweets accuse the department of submitting a "politically correct" version of the ban. Sessions stepped away after reports revealed that he spoke with Russian Ambassador Sergey Kislyak twice during the 2016 campaign and did not reveal those conversations during his confirmation hearing.
The feud between Donald Trump and Confederate elf statue Jefferson Beauregard Sessions III appears more serious by the day.
Trump hasn't seen it the same way, the Trump adviser said. The omission came on the advice of staff and an FBI investigator, the agency said.