Updated at 12:40 p.m. ET

Deputy Attorney General Rod Rosenstein said Tuesday that even if President Trump told him to fire Robert Mueller as special counsel overseeing the Department of Justice investigation into Russian meddling in the 2016 election, he would not follow the order unless he thought there was good cause.

The statement came after Sen. Susan Collins, R-Maine, asked Rosenstein during an open Senate Appropriations subcommittee hearing what he would do if Trump asked him to fire Mueller.

"Senator, I'm not going to follow any order unless I believe those are lawful and appropriate orders," Rosenstein said. "Special counsel Mueller may be fired only for good cause, and I am required to put that cause in writing. That's what I would do. If there were good cause, I would consider it.

"If there were not good cause, it wouldn't matter to me what anybody says."

Collins' question was prompted by recent media reports that Mueller's role leading the DOJ's Russia investigation could be in jeopardy.

Last night, a longtime friend of President Trump, Christopher Ruddy, said the president is considering firing Mueller.

"I think he is considering perhaps terminating the special counsel," Ruddy, who leads the conservative news website Newsmax, said on PBS NewsHour. "I think he's weighing that option. ... I personally think it would be a significant mistake, even though I don't think there is a justification [for a special counsel]."

The White House, however, said Trump and Ruddy have never discussed the issue. "With respect to this subject, only the president or his attorneys are authorized to comment," White House press secretary Sean Spicer told NPR.

Collins' question wasn't the only time the Mueller investigation came up during Rosenstein's hearing on Capitol Hill.

New Hampshire Sen. Jeanne Shaheen, a Democrat, opened her line of questioning, in the hearing that was supposed to focus on the Justice Department budget, by asking whether Rosenstein had seen any evidence of good cause to fire Mueller. After responding that he had not, Rosenstein reassured Shaheen of his confidence in the process.

"Director Mueller is going to have the full degree of independence that he needs to conduct that investigation appropriately," Rosenstein said.

Republicans in Congress are also shaking off the notion that Trump could fire Mueller.

"You're creating a debate that's not happening," said House Majority Leader Kevin McCarthy on Tuesday morning, responding to a reporter's question about the rumor.

The responsibility for appointing (or theoretically firing) Mueller lies with Rosenstein because his boss, Attorney General Jeff Sessions, recused himself in March from all investigations involving Russia and the 2016 elections.

At the time, Sessions said he was recusing himself only because he was involved in the 2016 campaign as an adviser to the Trump campaign. Doubt, however, has been cast on that explanation because of cryptic testimony from former FBI Director James Comey last week. Comey said he and other FBI officials expected Sessions to recuse himself before it was publicly announced but would not discuss why they came to that conclusion.

Sessions is testifying before the Senate Intelligence Committee on Tuesday afternoon.

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