Per the sources, Trump rattled off the same things he has been saying publicly — that his call with Zelensky was "perfect"and he did nothing wrong.

But he then threw Perry into the mix and said something to the effect of: "Not a lot of people know this but, I didn't even want to make the call. The only reason I made the call was because Rick asked me to. Something about an LNG [liquefied natural gas] plant," one source said, recalling the president's comments. 2 other sources confirmed the first source's recollection.

Why it matters: The president's remarks suggest he may be seeking to distance himself from responsibility or recast the pretext for the call. White House officials did not respond to requests for comment.

Another source on the call said Trump added that "more of this will be coming out in the next few days" — referring to Perry.

Worth noting: Text messages released this week between Trump administration officials and Andrey Yermak, a top aide to Zelensky, suggest that Trump's personal lawyer, Rudy Giuliani, was a primary advocate for arranging the call.

There is no mention in the text messages of Perry playing a role in making this call happen.

in the text messages of Perry playing a role in making this call happen. Zelensky talks about buying American oil and wanting to work with the U.S. on energy independence, but Perry and LNG are not discussed in the 5-page memo of the Trump-Zelensky call released by the White House.

Between the lines: Perry, who is reportedly resigning by the end of this year, has become increasingly embroiled in congressional Democrats' impeachment inquiry.

In May, Perry led a U.S. delegation to Ukraine for Zelensky’s inauguration in place of Vice President Mike Pence, and Democrats have begun to press Perry for more information about the trip and his conversations with Ukrainian leaders.

The House subpoena of Rudy Giuliani also seeks documents related to Perry's "involvement with Ukrainian leaders last spring."

However, Perry told the Christian Broadcasting Network on Friday that, "as God is my witness," neither Joe or Hunter Biden's name ever came up.

And as The Washington Post recently reported, "no evidence has emerged that Perry participated in the effort to pressure Ukrainian officials to investigate Joe Biden and his son, Hunter."

Perry's spokeswoman, Shaylyn Hynes, told Axios: “Secretary Perry absolutely supported and encouraged the president to speak to the new president of Ukraine to discuss matters related to their energy security and economic development."

"He continues to believe that there is significant need for improved regional energy security—which is exactly why he is heading to Lithuania tonight to meet with nearly 2 dozen European energy leaders (including Ukraine) on these issues,” Hynes added.

The White House acknowledged the conference call in a Friday readout that said participants included Minority Leader McCarthy, Whip Steve Scalise, Republican Conference Chair Liz Cheney, and GOP leaders on key House committees — and that they discussed Friday's jobs report, the economy and concerns about Democrats' impeachment inquiry.

The readout makes no mention of Rick Perry.

Go deeper: Politico examines Perry's ties to Ukraine.

Editor’s note: This post has been corrected to show that Kevin McCarthy is the House minority leader, not the majority leader.