Trump was also swayed by foreign allies, including Britain, in deciding to reverse course, these people said. It wasn't immediately clear what other governments may have raised concerns to the White House.
On Monday, the president ordered the Justice Department to declassify significant materials from the Russia investigation, a move that threatened another showdown with federal law enforcement officials resistant to publicizing information from an ongoing probe.
The White House issued a statement Monday saying Trump was ordering the department to immediately declassify portions of the secret court order to monitor former campaign adviser Carter Page, along with all interviews conducted as officials applied for that authority.
Trump also instructed the department to publicly release the unredacted text messages of several former high-level Justice Department and FBI officials, including former FBI director James B. Comey and deputy director Andrew McCabe.
For months, conservative lawmakers have been calling on the department to release Russia-related and other materials, many of them accusing law enforcement of hiding information that might discredit the Mueller investigation. Those calls were amplified by Fox News hosts, whom the president had previously cited as influencing his decision.
The president's declaration on Friday appears to indicate he is willing to let the Justice Department's inspector general - which is already conducting an internal investigation of how the Russia probe has been handled - review the material rather than release it publicly.
"Thankfully it seems that saner minds have prevailed, at least for the time being," said Sen. Mark Warner, D-Va. "This underscores why the President should be relying on the expertise and advice of intelligence and law enforcement professionals, not cable news hosts."