U.S. Secretary of State Mike Pompeo responded to President Trump's tweet Tuesday morning saying that the president would "love" for Pompeo to testify as part of the impeachment proceedings. The administration has declined to compel some current and former administration officials to testify, which Mr. Trump argues is because he is "fighting for future Presidents and the Office of the President."

"I would ... love to have Mike Pompeo, Rick Perry, Mick Mulvaney and many others testify about the phony Impeachment Hoax. It is a Democrat Scam that is going nowhere but, future Presidents should in no way be compromised," Mr. Trump tweeted, referring to his former Energy Secretary and current acting chief of staff.

Pompeo responded cryptically to Mr. Trump's tweet in a press conference later on Tuesday.

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"When the time is right, all good things happen," Pompeo said with a smile.

The secretary of state also deflected a question on whether the U.S. should investigate the debunked theory that Ukraine and not Russia hacked the Democratic National Committee (DNC) server during the 2016 election.

Pompeo, who was CIA director in the first year and a half of the Trump administration, responded, "Any time there is information that any country has messed with an American election, we not only have a right but a duty to make sure we chase that down."

"To protect our elections, America should leave no stone unturned," he continued. "So, whatever nation it is that we have information that so much as suggests that there might have been interference or an effort to interfere in our elections, we have an obligation to make sure that the American people get to go to the ballot box and cast their ballot in a way that is unimpacted by the malevolent actors trying to undermine our Western democratic values."

Mr. Trump has promoted the theory, although the intelligence community has concluded that Russia interfered in the 2016 election. The Mueller report, released earlier this year, described the Russian intelligence directorate (GRU) attacks on the DNC, as well as the DCCC and Hillary Clinton campaign chairman John Podesta.

Pompeo also declined to say whether Mr. Trump would sign a bill overwhelmingly passed by Congress requiring sanctions against China for any human rights abuses against Hong Kong.