Officials said Trump made the decision to scrap the CIA programme nearly a month ago, after an Oval Office meeting with CIA Director Mike Pompeo and National Security Adviser H.R. McMaster ahead of a July 7 meeting in Germany with Russian President Vladimir Putin.
Spokesmen for the National Security Council and the CIA declined to comment.
After the Trump-Putin meeting, the United States and Russia announced an agreement to back a new ceasefire in southwest Syria, along the Jordanian border, where many of the CIA-backed rebels have long operated. Trump described the limited ceasefire deal as one of the benefits of a constructive working relationship with Moscow.
Trump's dealings with Russia have been under heavy scrutiny because of the investigations into the Kremlin's interference in the 2016 election. The decision on the CIA-backed rebels will be welcomed by Moscow, which focused its firepower on those fighters after it intervened in Syria in 2015.
Some current and former officials who support the programme cast the move as a major concession.
"This is a momentous decision," said a current official. "Putin won in Syria."
With the end of the CIA programme, US involvement in Syria now consists of a vigorous air campaign against Isis (Islamic State) and a Pentagon-run train-and-equip programme in support of the largely Kurdish rebel force that is advancing on Isis strongholds in Raqqa and along the Euphrates River valley.
The Trump Administration's long-term strategy, following the defeat of Isis, appears to be focused on stitching together a series of regional ceasefire deals among the US-backed rebels, the Syrian Government and Russia.
Some analysts said the decision to end the programme was likely to empower more radical groups inside Syria and damage the credibility of the United States.
"We are falling into a Russian trap," said Charles Lister, a senior fellow at the Middle East Institute, who focuses on the Syrian resistance. "We are making the moderate resistance more and more vulnerable. . . . We are really cutting them off at the neck."
Others said it was recognition of Assad's entrenched position in Syria.
"It's probably a nod to reality," said Ilan Goldenberg, a former Obama Administration official and director of the Middle East Security Programme at the Centre for a New American Security.
US intelligence officials say battlefield gains by rebels in 2015 prompted Russia's direct military intervention on the side of the Assad regime. Some US officials and their allies in the region urged President Barack Obama to respond by providing the rebels with advanced antiaircraft weapons so they could better defend themselves. But Obama balked, citing concerns about the United States getting pulled into a conflict with Russia.
