House Intelligence Committee Chairman Adam Schiff Adam Bennett SchiffPelosi, Democrats unveil bills to rein in alleged White House abuses of power Chris Matthews ripped for complimenting Trump's 'true presidential behavior' on Ginsburg Trump casts doubt on Ginsburg statement, wonders if it was written by Schiff, Pelosi or Schumer MORE (D-Calif.) said Sunday that he believes the Republican Party has turned into a "cult" of President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE's personality and that GOP lawmakers likely wouldn't act in accordance with their Constitutional obligations.

Schiff made the comments on ABC's "This Week" while discussing the things Democrats should recognize while considering launching an impeachment inquiry.

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"In terms of the impeachment process, it’s not mandated by the Constitution," Schiff said. "We can avail ourselves of this when the president demonstrates acts that are high crimes or misdemeanors. It is certainly true, I think, that much of his conduct qualifies for that, but at the same time, we have to recognize the reality that one party, the Republican Party, has turned itself into a cult of the president's personality and is not likely to act consistent with its constitutional obligations."

House Intelligence Committee Chairman Adam Schiff on impeachment: "One party - the Republican Party has turned itself into a cult of the president's personality and is not likely to act consist with its constitutional obligations" https://t.co/1KA7z13fgZ pic.twitter.com/bZ6a673Fd5 — This Week (@ThisWeekABC) June 2, 2019

"And we have to figure out in that context, is this the right thing for the country, and I’m just not convinced, not yet, that that’s the case," Schiff said.

Many House Democrats called for the lower chamber to launch an impeachment inquiry against President Trump after special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE made a public statement about his investigation last week.

Mueller's report, which was released in April, did not find sufficient evidence to conclude a conspiracy between the 2016 Trump campaign and Russia took place. The report noted that Mueller could not reach a conclusive determination on whether Trump obstructed justice.

While delivering his first remarks about the probe, Mueller said that if the special counsel's office had "confidence that the president clearly did not commit a crime, we would have said so."

Mueller said he did not want to testify before Congress about his investigation, which Schiff said he was "disappointed" by.

"I think he has one last service to perform," he said. "It’s not enough merely to speak for 10 minutes and say, 'I’m not going to answer questions for the Congress and the American people.'"

Schiff added that there are "a great many things" not included in the report that the House would like to question Mueller about.