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

South Carolina Rep. Trey GowdyHarold (Trey) Watson GowdyTop House Dem claims Judiciary chairman's DOJ, FBI subpoena is invalid The Hill's Morning Report — Sponsored by PhRMA — GOP lawmakers race to find an immigration fix Republicans tear into IG finding on Clinton probe MORE (R) said President TrumpDonald John TrumpCNN analyst Kirsten Powers: Melania's jacket should read 'Let them eat cake' CNN's Cuomo confronts Lewandowski over 'womp womp' remark Sessions says FBI agent Peter Strzok no longer has his security clearance 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 RosensteinGrassley wants to subpoena Comey, Lynch after critical IG report Top House Dem claims Judiciary chairman's DOJ, FBI subpoena is invalid Republicans tear into IG finding on Clinton probe MORE to "bring an end to the alleged Russia collusion investigation."