President Donald Trump's first Homeland Security and counterterrorism adviser, who resigned after a year in the office, said on "This Week With George Stephanopoulos" on Sunday that he is "deeply disturbed" and "frustrated" by the "entire mess" that began in July with Trump's phone call with a young Ukrainian president and suddenly this week sparked a firestorm of calls in Congress to impeach the president following the disclosure of an extraordinary whistleblower complaint.

'The whole world is watching'

"I'm deeply disturbed by this as well, and this entire mess has me frustrated," said former Homeland Security advisor Tom Bossert, now an ABC News contributor.

"You and I lived through the impeachment of President [Bill] Clinton and saw how frustrating and dividing it could be and I just spend the week overseas and I'll tell you, the whole world is watching," Bossert said, gesturing to Stephanopoulos.

"You saw how frustrating and dividing it could be. The whole world is watching this. The removal of a president is a big and serious deal, but the removal of a president -- in not only a democracy but the biggest democracy -- is really a weighty matter and I hope that everyone can sift through the evidence and be careful, as I've seen a lot of rush to judgement this week," Bossert said.

But Bossert described the allegations against Trump as extremely serious.

"That said, it is a bad day and a bad week for this president and this country -- if he is asking for political dirt on an opponent," said Bossert.

"But it looks to me that the other matter, that's far from proven, was whether he was doing anything to abuse his power and withhold aid, in order to solicit such a thing," Bossert said, referring to a Ukrainian investigation into political rival Joe Biden and his family. "That seems, I think, far from proven and it's going to be the focus -- I think -- of our Congress for the next year."

'Completely debunked' theory

Bossert was sharply critical of Trump personal lawyer Rudy Giuliani, who was also a guest on the show. He expressed a combination of frustration and bewilderment that some members of the Trump team continue to spout debunked conspiracy theories about the hack of the Democratic National Committee [DNC] computer servers during the 2016 election campaign.

"It's not only a conspiracy theory, it is completely debunked. I don't want to be glib about this matter but last year, retired former Senator Judd Gregg wrote in The Hill magazine Five Ways or Three Ways to Impeach Oneself and the third way was to hire Rudy Giuliani."

"At this point, I am deeply frustrated with what he and legal team are doing in repeating that debunked theory to the president. It sticks in his mind when he hears it over and over again. And for clarity here, George, let me just repeat here, again, that it has no validity."

"The United States government reached its conclusion on attributing to Russia the DNC hack in 2016 before it even communicated it to the FBI. And long before the FBI ever knocked on the door at the DNC. So a server inside the DNC was not relevant to our determination to the attribution. It was made up front and beforehand. And so while servers can be important in some of the investigations that followed, it has nothing to do with the U.S. government attribution for the DNC hack."

Later in the program, Giuliani told Stephanopoulos: "Tom Bossert doesn't know what he's talking about."

Bossert, when asked to characterize his own interpretation of the call, said he read more into it than most observers because he spent a year discussing such matters with Trump, as his core responsibilities were election security and coordinating the response to Russian interference in the 2016 U.S. presidential elections.

"I didn't see, like others have seen, pressure in this call," Bossert said. "I understand why people are interpreting it that way, [but] I've spent a lot of time with this president, and I can easily see other reasons for why this president might have delayed aide to Ukraine and those Javelin missiles. As you know President [Barack] Obama considered this deeply and decided not to provide lethal military support. President Trump and I and others spent quite a bit of time talking about this. In fact, in the call itself -- although there are a lot of reasons he alludes to -- one that is quintessential Donald Trump. That is his frustration with Angela Merkel, the German nation member of NATO [North Atlantic Treaty Organization'] is doing nothing to help Ukraine, and he expressed some lamentation over that fact."

'Pound of flesh'

Still, Bossert said, he has some sense of the thinking in the White House.

"I honestly believe this president has not gotten his pound of flesh yet from past grievances on the 2016 investigation," Bossert said. "I believe he and his legal team probably even prior to Joe Biden announcing that he would run for president, and they are continuing to focus on everything they can in their belief -- understandably in this case -- that the president was wrongly accused of colluding with Russia the first time around. But George, if he continues to focus on that white whale, it's going to bring him down."

Bossert resigned from the administration in April 2018, one day after then Trump national security advisor John Bolton began his new role in the White House. Earlier this month, Trump said he ousted Bolton from the position over "very big mistakes" and policies disagreements, including decisions concerning the Middle East.

Bolton has countered that he offered to resign the previous day, but the president waved that offer away.

Bossert's comments come amid what is shaping up to be an exceptionally swift launch of a presidential impeachment inquiry.

House Intelligence Committee Chairman Adam Schiff told reporters Friday that his committee is mapping out potential hearings, depositions and subpoenas for its impeachment probe in the weeks ahead, as Democrats issued the first subpoena in an effort centered on President Trump's phone call with the president of Ukraine and a related whistleblower complaint.

Nearly two-thirds of Americans believe President Trump's encouragement of a foreign leader to investigate Trump's political rival and his family is a serious problem, but only 17% said they were surprised by the president's actions, according to a new ABC News/Ipsos poll.

The poll, conducted by Ipsos in partnership with ABC News, asked Americans about a July phone call between Trump and Ukrainian President Volodymyr Zelenskiy in which Trump urged his Ukrainian counterpart to work with his personal attorney Rudy Giuliani and U.S. Attorney General William Barr to investigate former Vice President Joe Biden and his son, Hunter, according to a memo released by the White House.

The high-velocity push toward an impeachment inquiry has jump-started Democratic consensus and unified a party long torn between what many observers see as political necessity and moral imperative, with a devastating but ultimately inconclusive report from the Mueller investigation in their rear view mirror and the snow-soaked cornfields of February's Iowa caucuses just up the road.

Trump has openly acknowledged that he discussed Biden in a call with Ukranian president but has characterized the call as perfectly acceptable presidential behavior. Yet, the growing appearance that a U.S. president sought to enlist a foreign in nation in investigating his political rivals has sharply -- and swiftly -- shifted the political dynamic in the nation's capital.

Editor’s Note: A prior version of this story incorrectly reported that George Stephanopoulos served in the Clinton White House during his impeachment. Stephanopoulos left the White House in 1996, two years prior to the impeachment proceedings.

ABC News' John Santucci and Katherine Faulders contributed to this report.