After repeated denials by the administration -- including by the president himself -- Mulvaney did not dispute to ABC News' Chief White House Correspondent Jonathan Karl that there was a quid pro quo in the Ukraine affair. He has since walked back the comments he made on Thursday during a White House briefing, writing in a statement that the press has "decided to misconstrue" his earlier comments.
When Stephanopoulos asked Pompeo on Sunday if it would be appropriate to put conditions on aid to Ukraine, Pompeo said he would not comment on a hypothetical.
"The chief of staff said it did," Stephanopoulos said.
"George, it -- you asked me if this happened," Pompeo said after a pause. "It's a hypothetical. I have told you what I observed, what I saw, the process related to this very funding."
Pompeo also would not comment Sunday on the role in Ukraine policy of Trump's personal attorney Rudy Giuliani, including his potential conflicts of interest, citing his policy of not commenting on internal deliberations in the administration.
"But -- but this was different," Stephanopoulos pressed. "This was not a member of the administration. This is the president's personal lawyer, who was pursuing this as -- at the president's direction and -- and going around the normal State Department procedures."
"George, private citizens often are part of executing American foreign policy," Pompeo said, referring to past envoys such as former New Mexico Gov. Bill Richardson who worked overseas on behalf of Democratic administrations. "You know that."
He also said that he did not review Giuliani's dossier of materials from Ukraine, instead passing it on to the appropriate people within the State Department.
Separately, Pompeo said he would not comment on the circumstances around former Ambassador to Ukraine Marie Yovanovitch's removal, but noted that she was only withdrawn from her post a few weeks early and still works at the State Department.
"Ambassadors serve at the pleasure of the president, and when a president loses confidence in an ambassador -- it's not in that ambassador, the State Department or America's best interest for them to continue to stay in their post," he said.
When Pompeo was asked about his former senior adviser Michael McKinley 's testimony on Wednesday, that he left the State Department over her removal, the secretary of state said, "I never heard him say a single thing about his concerns with respect to the decision that was made … not once."
When Stephanopoulos asked Pompeo about the testimony of several State Department officials, Pompeo said it wouldn't be appropriate to comment on personnel decisions.
"George, in good time all of the facts surrounding each of these incidents will become clear. But it's not appropriate for me to comment on all of the things that happen inside of personnel decisions -- none -- none of our foreign service officers would welcome the secretary of state talking about why someone stayed, why someone was removed, why someone was transferred. It wouldn’t be appropriate," he said.
Pompeo did disagree with Mulvaney's commenting that State Department officials who have testified as a part of the impeachment inquiry were doing so because they disagreed with the president's politics.
"Each of us has a solemn responsibility to defend the Constitution and to speak the truth," Pompeo said on "This Week." "I said this the other day, I hope those officers who go to Capitol Hill will speak truthfully, that they'll speak completely."
He did, however, call Intelligence Committee Chairman Adam Schiff's investigation a "kangaroo court," and pushed back on information released from closed-door testimonies as "leaked reporting from Democrats."
ABC News has reported on disgruntled career State Department employees, upset over the treatment of Yovanovitch and other perceived lack of support.
"We've done great things for these officers," Pompeo responded. "I see these stories about morale being low, I see things precisely the opposite. I see motivated officers."
Last month, the secretary was subpoenaed as a part of the impeachment inquiry against Trump and he has accused Democrats of attempting to "bully" State Department officials. He was listening to the July call between Trump and Ukrainian President Volodymyr Zelenskiy -- which is at the center of the complaint -- ABC News reported earlier this month.
When asked Sunday if he would testify as a part of the inquiry if called to do so, Pompeo said "I've said all along, I'll do everything I'm required to do by law."