Schiff says that if Trump fires Mueller, Congress might name its own independent counsel to investigate the case.
White House spokesman Sean Spicer did not explicitly endorse Sessions' appearance, saying in response to a question, "We're aware of it, and we'll go from there".
Trump can not directly dismiss Mueller.
On Monday, Christopher Ruddy, a longtime Trump friend, said in an interview on PBS that he had just come from the White House and that the president was "considering, perhaps, terminating the special counsel". Conservative Review contributor Steve Deace labeled calls to fire Mueller the "absolutely dumbest dumbassery" in a series of tweets Monday night.
Yet it's a line of thinking that is making its way to the president's ears. I knew him before that, and I have confidence in Mr. Mueller, ' the attorney general said. Attorney General Jeff Sessions, who is set to testify before the Senate intelligence committee today, has recused himself from the investigation.
"You have my assurance that we are going to faithfully follow that regulation", he said, "and director Mueller is going to have the full degree of independence that he has to conduct that investigation appropriately".
"Special counsel Mueller may be fired only for good cause, and I am required to put that cause in writing".
The former Federal Bureau of Investigation director also testified that the agency had believed Sessions was "inevitably going to recuse" for reasons he could not elaborate on. Gingrich said he is troubled by Democratic donations of Mueller's picks to help lead the probe.
After initially being praised by Republicans and Democrats for his integrity, Mueller has had his impartiality as special counsel questioned by some Trump supporters in recent days.
Rosenstein said he was also unaware of any "secret plan" to get rid of Mueller. The person demanded anonymity to discuss strategy on the sensitive matter. "I don't give the benefit of the doubt to somebody who could only hire Democrats but claims we ought to trust him". But the president is going to seek the advice of his counsel and inside the government as well as outside. Still, he added, "I can't imagine that that issue is going to arise". Although Ryan did not say such a Trump move would be unacceptable, his endorsement of Mueller was one of the few times the speaker has sent such a preemptive message to the administration since Trump became president.
In 1973, amid the Watergate scandal, President Richard Nixon ordered Attorney General Elliot Richardson to fire special prosecutor Archibald Cox.