AMMAN (Reuters) - Two Western-backed Syrian rebel groups fighting the Syrian army and Iranian-backed militias in southeastern Syria have been asked by their Western and Arab backers to pull out of the area and retreat into Jordan, rebels and diplomatic sources said on Sunday.

Both Usoud al-Sharqiya and Martyr Ahmad Abdo, part of the Free Syrian Army group, said they were told to end fighting in the area by their backers from the U.S. Central Intelligence Agency and neighboring states that support them, which include Jordan and Saudi Arabia.

“There is a official request for us to leave the area,” said Badr al Din al Salamah, a senior official in the Usoud al Sharqiya group, one of the main rebel groups in the area and a recipient of the military aid from the U.S.-backed alliance.

Since early this year, the rebels have pushed Islamic State militants out of a large swathe of sparsely populated territory stretching some 50 km (30 miles) southeast of Damascus, all the way to the Iraqi border along the frontier with Jordan.

But an offensive by the Syrian army, backed by Iranian militias and heavy Russian air cover, has encircled the rebels and eroded their gains. In recent weeks, the army has regained a string of border posts with Jordan that it had abandoned in the early years of the conflict

Western diplomatic sources said the request was tied to a decision by the administration of U.S. President Trump in July to halt the CIA’s program to equip and train rebel groups fighting the government of Syrian President Bashar al-Assad.

The CIA program began in 2013 as part of efforts by the administration of then-President Barack Obama to overthrow Assad. The Trump administration says its strategy in Syria is focused only on defeating Islamic State.

In a letter purportedly to rebel commanders and seen by Reuters, they were told they although they had fought bravely to fend off the Syrian army, their presence in a small enclave now posed a threat to them.

The decision has caused disaffection among hundreds of fighters in the two groups, who consider withdrawing into Jordan as effectively disbanding their forces.

The two groups, who have hundreds of fighters, will have to hand over heavy artillery and dozens of U.S.-made anti-tank missiles that played a part in their battlefield successes against Islamic State and the Iranian-backed militias, rebels say.

In a meeting on Saturday, the rebel commanders told the joint operations center in Jordan that requested their withdrawal they would rather “stay and die” in the desert than leave the battlefield.

“We have rejected the request, since if we entered Jordan we would consider it the end ... the blood of our martyrs has not dried yet,” said al-Salameh.

The military operations center has not offered them a choice to move to a U.S. garrison further east near the border with Iraq in Tanf, the rebels say. That garrison, run by a separate program of the Pentagon, hosts an Arab rebel tribal group known as the Maqhawir al Thwra.

Another rebel official said they were not necessarily opposed to withdrawing, but they wanted assurances from Jordan they could lobby to expand to the Badia area a U.S.-Russian-brokered ceasefire, which has halted fighting in southwest Syria.

Washington and Jordan are currently negotiating with Moscow to implement a de-escalation zone that would push back Iranian-backed forces 40 kms north of the border strip with Jordan, diplomats say.

“We have accepted in principle and there are matters that have to be resolved. But until this moment there is no final agreement on withdrawing and we are still in the Badia and still fighting and in our posts,” said Said Seif, a spokesman of the Martyr Ahmad Abdo group.