American officials said there appeared to be no direct connection between the two events, but they underscored the complexity of a region in which Syria, Russia, Turkey, Iran, Israel and the United States with its allies have carried out air or missiles strikes, albeit in pursuit of different and often competing objectives.
For the United States, the main focus has been battling the Islamic State, also known as ISIS or ISIL. This month Syrian Kurdish and Arab fighters, supported by American advisers and air power, began the battle for Raqqa, the militants’ self-declared capital.
Even before that battle is over, however, tensions have risen over control of eastern Syria as Iranian-backed militias, including the Lebanese group Hezbollah, have moved to extend their reach toward areas where the American-based fighters are also operating.
Not only are forces loyal to Mr. Assad interested in controlling the oil-rich Deir al-Zour province and relieving the pressure on a Syrian military garrison that has been surrounded there, but the Iranian-backed Shiite fighters are widely believed to be trying to link up with Iranian-backed militias in Iraq and establish a supply corridor that runs from Syria to Iraq and, eventually, to Iran.
The episode on Sunday began around 4:30 p.m. local time when American-backed ground Syrian fighters, who are officially called the Syrian Democratic Forces, came under attack by what the Pentagon described only as “pro-Syrian regime forces” and were forced from their positions in the town of Ja’Din, south of Tabqah. Several of the American-supported fighters were wounded.
To scare away the adversary forces, American warplanes buzzed the pro-Assad troops in what the Pentagon called a “show of force.” That appeared to put an end to the fighting, and the Americans sought to defuse the situation by calling their Russian counterparts from Al Udeid Air Base in Qatar.
But the Syrians were not finished. At 6:43 p.m., a Syrian SU-22 warplane dropped several bombs near the American-backed fighters. Attempts to warn the Syrian plane away from the area using an emergency radio frequency failed, said Col. John J. Thomas, the spokesman for the United States Central Command, which oversees American military operations in the Middle East.
An F/A-18 “Super Hornet,” which was patrolling the area after launching from the George H. W. Bush aircraft carrier, quickly shot down the Syrian plane. American advisers were not in the immediate vicinity of the bombing by the Syrian SU-22.
A statement by the American-led task force that is fighting the Islamic State stressed that it was taken under rules of engagement permitting the “collective self-defense” of its Syrian partners.
The United States has set up a garrison at al-Tanf in southeastern Syria, where Syrian fighters and American, British and Norwegian advisers have been based.
The United States has warned pro-Assad forces to stay out of a “deconfliction” zone it has declared around the garrison. The town of Ja’Din is little more than a mile north of this deconfliction area, but the United States has made it clear that the Syrian fighters it supports and the American and other allied advisers that accompany them are not limited to that buffer area.
After Sunday’s episode, the American-led task force said it was not seeking a confrontation with Mr. Assad or the Iranian, Russian or Shiite militias that are fighting to support the Syrian leader — but added that it would defend the forces it has assembled to pursue the Islamic State.
“The coalition’s mission is to defeat ISIS in Iraq and Syria,” the official statement said. “The coalition does not seek to fight Syrian regime, Russian, or pro-regime forces partnered with them, but will not hesitate to defend Coalition or partner forces from any threat.”
Iran offered official statements about its military actions, too, and a video of the launch of one of the missiles was posted by the semiofficial Fars News Agency.
The Guards Corps said the strike, sending missiles flying over neighboring Iraq into Syria, had been carried out in retaliation for the terrorist attacks this month on the Iranian Parliament and the shrine of the founder of the Islamic Republic. Eighteen people died in those attacks and dozens were wounded. The Islamic State claimed responsibility.
The Iranians made no effort to offer warnings about or “deconflict” their missile strike with the United States, American officials said. The Iranian missile attack was seen by analysts as a sign of an escalating role for Iran in the Syrian conflict and an indication of Tehran’s growing power in the region.
The missile strike over a considerable distance may have also been designed to send a message to Iran’s enemies in the region, including Israel and Saudi Arabia, as well as the United States, which maintains multiple military bases in the Middle East.