Rep. Trey Gowdy broke with President Trump on where the controversial House Intelligence Committee memo leaves special counsel Robert Mueller and his Russia inquiry.

While Trump tweeted Saturday morning that the memo "totally vindicates" him in regards to the federal Russia inquiry, Gowdy, a key player in the development of the report, said he doubts Mueller's probe, which is looking into possible collusion between members of Trump's campaign and the Kremlin, will be impacted.

"I would say this. I'm sure the president is frustrated," Gowdy, R-S.C., said in an interview for CBS News' "Face the Nation" when asked about Trump's tweet. "You know, [House Intel ranking member] Adam Schiff prejudged the investigation before we interviewed the first witness, so I — I'm sure that that instructs some of what he said. I — I actually don't think it is has any impact on the Russia probe for this reason —."

In the run-up to the release of the memo, which outlines alleged abuses of surveillance authority by the U.S. government, Trump defenders had suggested that it could damage the integrity of the Mueller investigation. Even after its release, some of his biggest supporters are still calling for Mueller to quit.

However, a key point in the memo concedes that the FBI began its formal investigation into the Trump campaign in July 2016 because of foreign policy aide George Papadopoulos, and not the salacious and largely unverified "Trump dossier" as some Republicans had prevously asserted. Papadopoulos pleaded guilty in October to charges brought against him by Mueller in his Russia investigation for lying to the FBI about his contacts with Russians.

Pressing the point, CBS News White House and senior foreign affairs correspondent Margaret Brennan asked: "The memo has no impact on the Russia probe?"

"Not to me, it doesn't — and I was pretty integrally involved in the drafting of it," Gowdy, a former federal prosecutor, said. "There is a Russia investigation without a dossier. So to the extent the memo deals with the dossier and the FISA process, the dossier has nothing to do with the meeting at Trump Tower. The dossier has nothing to do with an email sent by Cambridge Analytica. The dossier really has nothing to do with George Papadopoulos' meeting in Great Britain. It also doesn't have anything to do with obstruction of justice. So there's going to be a Russia probe, even without a dossier."

In regards to the FISA process, Gowdy was referring to a point stressed in the memo that claimed FBI Deputy Director Andrew McCabe testified in a private session with House Intel that the agency would not have pursued placing a Trump campaign adviser, Carter Page, under surveillance without the "Trump dossier" written by ex-British spy Christopher Steele. The memo also stressed that DOJ officials knew Steele had an anti-Trump bias but made no mention of that in their effort to renew FISA surveillance on Page.

After the release of the memo, Democrats appear to be spooked about Trump possibly interfering with the Mueller investigation, which Trump has repeatedly referred to as a "witch hunt."

While Trump doesn't have direct authority to fire Mueller, which he reportedly ordered but then backed away from last summer, he can fire the man who does oversee the Russia probe — Deputy Attorney General Rod Rosenstein.

With the release of the memo, devised by staffers under House Intel Chairman Devin Nunes, R-Calif., and a recent report that said Trump asked Rosenstein about the direction Mueller’s investigation was heading and whether he was “on my team," Democrats are keen to stop any attempt to get rid of Rosenstein, potentially as a ploy to eventually get rid of Mueller.

Top congressional Democrats warned Trump on Friday against using memo as a pretext to fire Rosenstein and therefore halt the Russia investigation, creating a “constitutional crisis.” The White House says Trump has no plans to fire Rosenstein.

Meanwhile key Republicans, including House Speaker Paul Ryan, R-Wis., have echoed Gowdy's reassurances. Ryan said this week that the memo "does not impugn the Mueller investigation or the deputy attorney general."

Gowdy, who announced last week that he would not seek re-election in 2018, is one of a few lawmakers who has seen the underlying documents that support the memo, and which Democrats have warned are needed to provide context to the assertions made in the document released Friday.

Rep. Jerold Nadler, D-N.Y., the top Democrat on the House Judiciary Committee who has viewed the underlying documents, wrote a letter to Democratic colleagues on Saturday that warned Rosenstein had become a "target for those attempting to interfere with that investigation."