Ruddy told ABC News that he stands by his comments that the president is considering asking Rosenstein to terminate Mueller. “Trump is definitely considering it ... it’s not something that’s being dismissed,” Ruddy said.
The notion was dismissed by senior White House aides later Monday evening, who said that Ruddy does not speak for the president, but it was not met with a denial. However, Principal Deputy White House Press Secretary Sarah Huckabee Sanders told reporters Tuesday that “while the president has the right to [fire Mueller], he has no intention to do so.”
"Mr. Ruddy never spoke to the president regarding this issue,” Spicer said in a statement. “With respect to this subject, only the president or his attorneys are authorized to comment."
Ruddy, today, took issue with Spicer's statement, arguing he should be focusing on the president’s achievements, not attempting to undermine "one of your few allies."
“Spicer issued a bizarre late night press release that a) doesn't deny my claim the president is considering firing Mueller and b) says I didn't speak to the president about the matter -- when I never claimed to have done so," Ruddy wrote in a text message sent to ABC News.
Ruddy continued, "Memo to Sean: Focus your efforts on exposing the flim-flam Russian allegations against POTUS and highlighting his remarkable achievements! Don't waste time trying to undermine one of your few allies.”
Ruddy later spoke to CNN, saying, "I wouldn't say I was fighting with Sean Spicer. I think that Sean is again doing something unusual and different, which is making a news story where one doesn't exist."
He argued that Jay Sekulow, a member of Trump's personal legal team, "went on TV this weekend and said the president was leaving open the option of terminating Robert Mueller as the special counsel."
"And I said that the president was indeed considering that. I never said that the president told me," Ruddy continued. "I never said I had a conversation. I never implied."
Sekulow said in an exclusive interview on “This Week" Sunday he was "not going to speculate" on whether the president may order the firing of the special counsel investigating Russia's meddling in the 2016 election and its possible ties to Trump associates, but added he “can't imagine the issue is going to arise.”
"I'm not going to speculate on what [Trump] will or will not do" with regard to Robert Mueller, the special counsel leading the FBI’s Russia probe, Sekulow told ABC News Chief Anchor George Stephanopoulos.
"Right now the role of the president is to govern the United States of America. He's going to do that. He's going to leave anything else to the lawyers. But I can't imagine that that issue is going to arise" with Mueller, said Sekulow.
In his interview with CNN, Ruddy added that he always speaks for himself, not the president. "He has his own spokesman," Ruddy told CNN. "Although I think they are in need of help from time to time."
When asked if the president interviewed Mueller for FBI director and if he has confidence in him now, Sarah Sanders told reporters Tuesday, "I do know that he did interview him the day before he was named the special counsel and beyond that, what I said earlier, I don’t have anything to add.”
ABC News' George Stephanopoulos contributed to this report.