He wrote: "The Mueller probe should never have been started in that there was no collusion and there was no crime". He said Mueller is as straight an arrow as there is in America, a former marine, and a Republican.
Gowdy, who is chairman of the House Oversight Committee and sits on the Intelligence and Judiciary committees, said he believed Dowd had done the President "a disservice" by releasing a statement saying he prays that Deputy Attorney General Rod Rosenstein will end the investigation led by former FBI Director Robert Mueller. Brennan asked him about McCabe's firing by Attorney General Jeff Sessions, Trump's complaints about the Mueller probe and what Gina Haspel, Trump's nominee for the top Central Intelligence Agency post, who played a role in the torture of terrorism suspects. "I think the White House has said 10 times, maybe more, that they're not going to fire Robert Mueller, they want him to be able to finish the investigation".
The tweets have put lawmakers on edge, particularly members of Mr. Trump's own party, for fear that he may fire Mueller.
McCabe's memos could factor into Mueller's investigation as his team examines Trump campaign ties to Russian Federation and possible obstruction of justice.
He said Trump would have trouble getting a replacement for the former Alabama senator through the Senate confirmation process.
"As I've said before, if he tried to do that it would be the beginning of the end of his presidency because we're a rule of law nation", he said on CNN.
But Republican Senator Lindsey Graham said Mr Mueller should be allowed to proceed without interference, and that many Republicans shared his view.
Pressed on the issue, Paul said he would not "advocate" for Trump to try to force Mueller out, just as he "would have never advocated for the appointment of a special prosecutor".
Mr. Comey, who was sacked in May, told Congress he kept detailed notes on each of his interactions with Mr. Trump, including a meeting in which the president allegedly told the lawman to lay off former National Security Advisor Michael Flynn, who was ousted for misleading Vice President Mike Pence about phones calls with Russian Ambassador Sergey Kislyak.
James Lankford, R-Okla., told ABC on "This Week".
Mr McCabe had been under internal investigation by the FBI and had already stepped down from his deputy post in January pending the review.
Although the decision to fire Mr McCabe was made by Mr Sessions, Mr Trump had criticised him for months.
He welcomed the news of his dismissal nearly immediately after Mr Sessions announced it, calling the move a "great day for democracy".
News that Mr McCabe had kept records of his conversations with Mr Trump at the time he was acting Federal Bureau of Investigation director emerged on Saturday.
"The Fake News is beside themselves that McCabe was caught, called out and fired".
His former boss James Comey, who Trump fired previous year , has testified that he kept similar notes.
He, too, has said he kept contemporaneous notes of his dealings with the president.
Axios reports the McCabe memos corroborate Comey's account of his own firing. McCabe has denied the conclusions.
"I am being singled out and treated this way because of the role I played, the actions I took, and the events I witnessed in the aftermath of the firing of James Comey", his response said.