Deputy Attorney General Rod Rosenstein, who named Mueller to lead the investigation into whether the Trump campaign colluded with Russia, testified there was no reason to dismiss him, and said that he alone has the authority to do so.
Asked in a Senate Appropriations Committee hearing if there was any cause to fire Mueller, Rosenstein flatly replied: "No."
"As long as I'm in this position, he's not going to be fired without cause," he added.
"I'm not going to follow any orders unless I believe those are lawful and appropriate orders."
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"I appointed him. I stand by it... And I am going to defend the integrity of that investigation," he said.
Rosenstein said he was also unaware of any "secret plan" to get rid of Mueller.
Yesterday, a close confidant of Trump, Newsmax website chief executive Chris Ruddy, said following a White House visit that the president is considering firing Mueller.
The White House downplayed Ruddy's comments. "Mr Ruddy never spoke to the president regarding this issue," an official said.
But the investigation by the Justice Department and probes carried out by two congressional committees have moved closer to the president, with Trump's son-in-law Jared Kushner and other former campaign staff having received requests and subpoenas for information from investigators.
Speaking earlier, House Speaker Paul Ryan said politicians should allow the special counsel to do his work.
"I think the best thing to do is to let Robert Mueller do his job. I think the best vindication for the president is to let the investigation go on independently and thoroughly.
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