"I felt that I was required to under the rules of the Department of Justice", he told the committee on Tuesday, adding that he gradually realised he would have to step down.
Chris Ruddy, a longtime Trump pal, told PBS's Judy Woodruff that Trump is "considering perhaps terminating" Robert Mueller, who was appointed as special counsel after Trump fired Federal Bureau of Investigation director James Comey.
Rosenstein responded, "Senator, I'm not going to follow any orders unless I believe those orders are lawful and appropriate orders". Mueller was appointed by US Deputy Attorney General Rod Rosenstein to probe into alleged Russian interference in the 2016 US polls.
Firing Mr. Mueller would be a politically explosive move that would raise new questions about Mr. Trump, whose abrupt dismissal of James Comey as FBI Director generated accusations of obstruction of justice and led to Mr. Mueller's appointment.
A friend of the president says Donald Trump is considering "terminating" special counsel Robert Mueller. Ruddy, a close Trump ally, told PBS NewsHour on Monday that the president is weighing the option.
It took about 24 hours, but the White House has knocked down speculation that President Donald Trump considered firing special prosecutor Robert Mueller.
"We're not going to let the President choose who conducts this investigation", he said.
Peter Carr, a spokesman for Mueller, declined to comment on Ruddy's remarks.
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Even so, Gingrich said, Trump won't seek to dismiss Mueller because he's confident the probe will conclude he's done nothing wrong.
Trump has the power to unilaterally remove Mueller from the job, but legal experts argue that would create a crisis in American institutions.
But Ruddy on Tuesday opened a new line of questions about Mueller's impartiality - the fact that Trump had considered Mueller for the Federal Bureau of Investigation director's job before he was named special counsel.
Sessions is testifying before the Senate Intelligence Committee on Tuesday afternoon. And if there were good cause, I would consider it.
Mr Rosenstein is charged with Mr Mueller's fate because Attorney General Jeff Sessions recused himself from all matters having to do with the Trump-Russia investigation.
To clamp down on the issue, Spicer released a statement Monday night saying that Ruddy had not spoken to the president about the issue and that only the president and his attorneys can comment on Mueller. Trump can rescind the regulation that establishes the burden of "good cause" for such a firing, or he could simply fire Rosenstein and install someone more to his liking.
But after the evidence of former Federal Bureau of Investigation director James Comey last week, Mr Gingrich said he had changed his mind.
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