A military alliance fighting in support of President Bashar al-Assad threatened on Wednesday to hit U.S. positions in Syria, warning its "self-restraint" over U.S. air strikes would end if Washington crossed "red lines".

The threat marks an escalation of tensions between the United States and the Syrian government and its backers over control of Syria's southeastern frontier with Iraq, where Washington has been training Syrian rebels at a base inside Syrian territory as part of its campaign against Islamic State militants .

The area is seen as crucial to Assad's Iranian allies and could open an overland supply route from Tehran to Iraq, Syria and Lebanon - the "Shia crescent" of Iranian influence that is a major concern to U.S.-allies in the region.

Tensions have been growing in southeastern Syria over the last several weeks. The United States launched air strikes on Tuesday against what it said were pro-government forces who it said posed a threat to U.S. and U.S.-backed forces in the area, the second such air strike in three weeks.

The statement from the pro-Assad alliance was issued in the name of the "commander of the operations room of the forces allied to Syria", and was circulated by a military news unit run by the Lebanese group Hezbollah, one of Assad's military allies.

The statement did not spell out whether Russia, Assad's most powerful ally, was a signatory. Speaking in Baghdad, a U.S. envoy said the United States was counting on regular contacts with Moscow to help avoid a conflict with pro-Damascus forces in the southeastern region known as the Badia.

Separate remarks by Syria's foreign ministry, carried by state TV, warned of the "dangers of escalation" and demanded the U.S. coalition stop strikes on Syrian soil.

The statement from the "allies of Syria" said attacks on U.S. forces could be carried out with "different missile and military systems, in the light of the deployment of American forces in the region".

"America knows well that the blood of the sons of Syria, the Syrian Arab Army, and its allies is not cheap, and the capacity to strike their positions in Syria, and their surroundings, is available when circumstances will it," the statement said.

It added that the silence of "the allies of Syria" thus far was "an exercise in self-restraint" to allow for "other solutions". "This will not last if America goes further, and crosses the red lines," it said.

In an apparent message to show the capabilities of Damascus backer Iran, Hezbollah aired what it said was footage taken undetected by an Iranian drone of a U.S. drone flying over southeastern Syria.

'Hostile Forces'

The U.S. military, which has sought to stay out of Syria's civil war and focus its firepower on Islamic State militants in Syria and Iraq, has repeatedly warned pro-Assad forces to stay away from a so-called "de-confliction" zone around their garrison near the southern Syrian town of al-Tanf.

Brett McGurk, the U.S. envoy to the international coalition against Islamic State militants , said the air strike on Tuesday was meant to defend American forces.

"We really do depend upon the Russians through our de-confliction military channels ... to help work these things out, and so we hope obviously that will not happen again," he said.

The U.S.-led coalition said that ahead of Tuesday's air strike there had been communications with Russia over allowing pro-government forces into the de-confliction zone to evacuate personnel wounded in an attack by an insurgent group.

In comments to Reuters, the coalition said it had agreed to the request and four unarmed trucks were observed evacuating the wounded personnel from the area, where Islamic State has previously mounted attacks.

"Later, at a separate location in the de-confliction zone, the coalition observed a large Syrian pro-regime force enter the de-confliction zone," the coalition added.

"These forces were clearly hostile and comprised a tank, artillery, anti-aircraft weapons, armed technical vehicles and more than 60 soldiers, which were posing a threat to coalition and partner forces based at the al-Tanf garrison," it said.

"The coalition issued several warnings prior to conducting the strike on two artillery pieces, an anti-aircraft weapon and a tank."

Tensions in southern Syria have flared as the intensity of the Syrian war has died down in areas of western Syria covered by an agreement brokered by Russia, Turkey and Iran to ease the fighting.