Syrian rebels say the United States and its allies are sending them more arms to try to fend off a new push into the southeast by Iran-backed militias aiming to open an overland supply route between Iraq and Syria.

Tensions escalated in the southeastern region of Syria, known as the Badia, this month when government forces supported by Iraqi militias deployed in a challenge to rebels backed by President Bashar al-Assad's enemies.

This has coincided with a march towards the Syrian border by militias from Iraq. They reached the frontier adjoining northern Syria on Monday. A top Iraqi militia commander said a wider operation to take the area from Islamic State of Iraq and the Levant (ISIL) started on Tuesday.

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While in Iraq the US has fought alongside Iranian-backed Iraqi government forces and militias against ISIL, in Syria Washington has lined up against Assad's Iranian-backed government and wants to block a further expansion of Iranian influence with its regional allies.

Several rebel groups fighting under the Free Syrian Army (FSA) banner operate in sparsely populated Badia, where they captured swathes of territory from ISIL this year. US air raids on May 18 targeted Iran-backed fighters who had moved into the area.

Also in May, Damascus declared both the Badia and Deir Az Zor priorities of its campaign to re-establish its rule over Syria, which has been shattered by six years of war that have killed hundreds of thousands of people. The government is being helped by both Iran and Russia, while the opposition has been helped by the West and regional states that oppose Assad.

Rebels said military aid has been boosted through two separate channels: a programme backed by the Central Intelligence Agency (CIA), known as MOC, and regional states including Jordan and Saudi Arabia, and one run by the Pentagon.

"There has been an increase in the support," said Tlass Salameh, head of the Jaish Usoud al-Sharqiya, one of the FSA groups backed by the CIA-sponsored programme. "There's no way we can let them open the Baghdad-Damascus highway," he said.

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A senior commander of a Pentagon-backed group, Maghawir al-Thawra, told Reuters news agency a steady flow of weapons had arrived at their base near the Iraqi border since the pro-Damascus forces began deploying this month.

He said efforts to recruit and train local fighters from Deir Az Zor had accelerated at their garrison at Tanf, on the highway some 20km from the Iraqi border.

"The equipment and reinforcements come and go daily ... but in the last few weeks they have brought in more heavy military vehicles, TOW [missiles], and armoured vehicles," he said, speaking on condition of anonymity.

Two armoured vehicles newly delivered to the Tanf garrison were shown in photos sent to Reuters from a rebel source. A video showed fighters unpacking mortar rounds.

In a written response to emailed questions, a spokesman for the US-led coalition did not say if coalition support to Maghawir al-Thawra had increased.

Colonel Ryan Dillon said coalition forces were "prepared to defend themselves if pro-regime forces refuse to vacate" a de-confliction zone around Tanf.

"The coalition has observed pro-regime forces patrolling in the vicinity of the established de-confliction zone around the Tanf training site in Syria ... Pro-regime patrols and the continued armed and hostile presence of forces inside the ... zone is unacceptable and threatening to coalition forces," Dillon said.

US jets this week dropped leaflets on pro-government forces instructing them to pull out of the Tanf area to the Zaza junction further from the border. The leaflets were obtained by Hammurabi Justice, a Maghawir-linked website.

The Syrian army could not be reached for comment.

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A commander in the military alliance fighting in support of Assad said the deployment of government forces and pro-Damascus Iraqi fighters in Badia would "obstruct all the plans of the MOC, Jordan and America".

The commander, a non-Syrian, said Assad's enemies were committed to blocking "what they call the [Shia] Crescent". But, he said, "Now, our axis is insistent on this matter and it will be accomplished."

The Iraqi Badr militia said its advance to the Syrian border would help the Syrian army reach the border from the other side.

"The Americans will not be allowed to control the border," its leader, Hadi al-Amiri, told al-Mayadeen TV.