Those calls -- both with leaders who maintain controversial relationships with Trump -- were among the presidential conversations that aides took remarkable steps to keep from becoming public.
In the case of Trump's call with Prince Mohammed, officials who ordinarily would have been given access to a rough transcript of the conversation never saw one, according to one of the sources. Instead, a transcript was never circulated at all, which the source said was highly unusual, particularly after a high-profile conversation.
The call - which the person said contained no especially sensitive national security secrets -- came as the White House was confronting the murder of journalist Jamal Khashoggi
, which US intelligence assessments said came at the hand of the Saudi government.
With Putin, access to the transcript of at least one of Trump's conversations was also tightly restricted, according to a former Trump administration official.
It's not clear if aides took the additional step of placing the Saudi Arabia and Russia phone calls in the same highly secured electronic system that held a now-infamous phone call with Ukraine's president
and which helped spark a whistleblower complaint made public this week, though officials confirmed calls aside from the Ukraine conversation were placed there.
But the attempts to conceal information about Trump's discussions with Prince Mohammed and Putin further illustrate the extraordinary efforts taken by Trump's aides to strictly limit the number of people with access to his conversations with foreign leaders.
The White House did not comment about the limiting of access to calls with the Russian and Saudi leaders.
Officials said the practice began more than a year ago after embarrassing leaks revealed information about Trump's phone conversations with the leaders of Australia and Mexico. While it includes the highly secure system for particularly sensitive matters, it has also extended to limiting the number of individuals who are provided a transcript or are able to listen to the call.
Those efforts have come under scrutiny after the intelligence whistleblower alleged that White House officials took unusual steps
to conceal Trump's phone call with Ukraine's new president.
The complaint alleged the handling of the Ukraine call was "not the first time" that such steps had been taken "solely for the purpose of protecting political sensitive — rather than national security sensitive — information."
Administration officials say John Eisenberg, the White House deputy counsel for national security affairs and a national security legal adviser, directed the Ukraine transcript call be moved to the separate highly classified system, as detailed in the whistleblower complaint.
That system is normally reserved for "code word" documents that are extremely sensitive, such as covert operations.
Eisenberg also played a role in the early Justice Department handling of the whistleblower complaint
. Eisenberg was on an August 14 call with the general counsel of the intelligence agency where the complainant worked, and John Demers, the assistant attorney general for the Justice national security division, a US official briefed on the matter said.
During that call, the general counsel informed Eisenberg and Demers that there were concerns being raised about one of Trump's phone calls with a foreign leader. Eisenberg invited Demers and the intelligence agency's general counsel to review the transcript of the call, and Demers traveled to the White House the following day to review it. The general counsel of the intelligence agency declined to review the call, according to the official.
The White House acknowledged earlier Friday
that administration officials directed the Ukraine call transcript be filed in a highly classified system, confirming allegations contained in the whistleblower complaint.
In a statement provided to CNN, a senior White House official said the move to place the transcript in the system came at the direction of National Security Council attorneys.
"NSC lawyers directed that the classified document be handled appropriately," the senior White House official said.
But the statement did not explain whether anyone else in the White House was part of the decision to put the Ukraine transcript in the more restrictive system. Nor did it delve into an accusation in the complaint that other phone call transcripts were handled in a similar fashion.
Like the call with Saudi's crown prince, the Ukraine transcript did not contain highly classified information to require such a move, raising questions about why the order was made.
The White House has not explained why it selectively put certain head of state calls into the codeword system, even when the content wasn't highly classified, such as the Ukraine call.
Officials from the past two administrations said it was unusual to transfer a transcript that doesn't contain sensitive information into the code word computer system.
"In my experience you would never move a transcript to the code word system if it does not have any code word terms. If the president is classifying and declassifying stuff he doesn't want to get out, that is an abuse of power and abuse of the system," said Sam Vinograd, a CNN national security analyst who served on President Barack Obama's National Security Council and at the Treasury Department under President George W. Bush.
Three other former National Security Council officials said they were unaware of calls that did not contain highly sensitive national security materials being moved into another location.
While the practice of limiting access to foreign leader calls began in earnest last year after the leaks of Mexico and Australian calls, it's not clear precisely when the initial steps were taken begin that effort.
The White House was also embarrassed when it was reported Trump had congratulated Putin on a phone call shortly after a Russian election widely seen as illegitimate. White House staff had written a memo specifically recommending Trump "do not congratulate" Putin in the call.
John Bolton, Trump's former national security adviser who departed from his post earlier this month, was known for keeping a tight hold on all information generally speaking, according to sources who worked with him at the NSC. He did not reply when asked for a request for comment through his spokesperson.
A former administration official said that despite the code word protection, you didn't necessarily need a special clearance to view the records and there was a process for officials to access the calls they wanted.
Trump's relationships with both Prince Mohammed and Putin have come under scrutiny over the past several years. Both are strongmen with dismal human rights records.
After Khashoggi was murdered at the Saudi consulate in Istanbul in October 2018, Trump vowed to get to the bottom of the matter. But he has repeatedly said he's unwilling to break off US-Saudi ties -- including military and trade — as a result.
With Putin, Trump has regularly worked arduously to guard his conversations, including asking for notes taken by his interpreter after their first encounter in 2017. He remains sensitive to accusations he's too cozy with the Russian leader who oversaw an election interference effort to get him elected.