Gowdy: Trump's lawyers doing 'disservice' by framing Mueller probe around collusion

South Carolina Rep. Trey GowdyHarold (Trey) Watson GowdyGowdy requests FEMA administrator’s travel records amid allegations Nunes: Russia probe documents should be released before election Gowdy: House Intel panel should release all transcripts from Russia probe MORE (R) said President TrumpDonald John TrumpTrump: I hope voters pay attention to Dem tactics amid Kavanaugh fight South Korea leader: North Korea agrees to take steps toward denuclearization Graham calls handling of Kavanaugh allegations 'a drive-by shooting' MORE's legal team is doing the president a "disservice" by framing Robert MuellerRobert Swan MuellerSasse: US should applaud choice of Mueller to lead Russia probe MORE's Russia probe around allegations that Trump's campaign colluded with Russia during the 2016 election.

"The notion that he [Mueller] was hired to only go look for criminality, I think, does a disservice to [the president]," Gowdy said in an interview with CBS News's "The Takeout" podcast.

Gowdy, who chairs the House Oversight and Government Reform Committee, said that Mueller's special counsel investigation extends beyond whether Trump's campaign colluded with Russia to how Russia sought to influence the 2016 election.

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Gowdy told CBS host Major Garrett that Trump's team should understand that the controversial dossier authored by Christopher Steele that makes salacious claims about Trump's ties to Russia was not the driving force behind the federal probe.

"I think his lawyers have done a disservice to him, frankly," Gowdy said. "I think allowing it to be framed as an investigation into collusion and collusion only, conflating the [former FBI Deputy Director] Andy McCabe firing, conflating, frankly, the dossier. This investigation would exist without a dossier. And I've said that for the last 12 months. With or without a dossier, this investigation goes on."

Gowdy went on to urge Trump to continue cooperating with the probe, despite what the White House has admitted is the president's "frustration" at the length of the investigation.

"There's a certain level of frustration that comes from anyone who is, quote, under investigation," Gowdy said. "If you believe you've done nothing wrong, you want the investigation concluded as quickly as possible. It is beyond argument that this has cast a pall over the first part of his presidency."

Speculation has grown over the last few weeks over whether Trump will fire Mueller in an attempt to end the investigation. The White House has repeatedly denied that Trump is considering firing the special counsel.

On Thursday, Trump's lead personal attorney handling the investigation, John Dowd, abruptly resigned, following news that Trump asked Deputy Attorney General Rod RosensteinRod Jay RosensteinDem lawmakers slam Trump’s declassification of Russia documents as ‘brazen abuse of power’ Time for sunshine on Trump-Russia investigation The Hill's Morning Report — Sponsored by United Against Nuclear Iran — Kavanaugh confirmation in sudden turmoil MORE to "bring an end to the alleged Russia collusion investigation."