BEIRUT — The struggle against the Islamic State group unfolded on two fronts Sunday: The U.S. military confirmed that it had shot down a Syrian air force jet that had bombed local forces aligned with the Americans, threatening to escalate tensions, and U.S.-backed Iraqi troops pushed into the last Islamic State stronghold in Mosul, launching a major battle for the Old City.

The U.S. had not shot down a Syrian regime aircraft before Sunday's confrontation, said Navy Capt. Jeff Davis, a Pentagon spokesman.

While the U.S. has said since it began recruiting, training and advising what it calls moderate Syrian opposition forces to fight the Islamic State group that it would protect them from potential Syrian government retribution, this was the first time it resorted to engaging in air-to-air combat to make good on that promise.

The U.S.-led coalition headquarters in Iraq said in a written statement that a U.S. F-18 Super Hornet shot down a Syrian government SU-22 after it dropped bombs near the U.S. partner forces, known as the Syrian Democratic Forces, wounding a number of the allied militiamen.

The plane went down near Tabqa, a Syrian town in an area that has been a weeks-long focus of fighting against Islamic State militants by the SDF as they surround the city of Raqqa and attempt to retake it.

The U.S. military statement said it acted in “collective self defense” of its partner forces and that the U.S. did not seek a fight with the Syrian government or its Russian supporters.

The Syrian military said the plane crashed and the pilot is missing.

In Iraq, the push for the Old City is the final major fight of an eight-month campaign to drive the militants from the nation’s second-largest city. The extremists are expected to make their last stand in the densely populated quarter with narrow, winding alleys.

Some 150,000 civilians are believed to be trapped in the Old City and risk being used as human shields by the extremists.

Iraq state TV aired live footage showing thick black smoke rising from the Old City, with the sound of gunfire rattling inside. It said leaflets were distributed urging civilians to leave through five “safe corridors.”

The International Rescue Committee called on Iraqi forces and the U.S.-led coalition to “do everything in their power to keep civilians safe during these final stages of the battle for Mosul.”

The Islamic State group captured Mosul when it swept across northern and central Iraq in the summer of 2014. Iraq launched a massive operation to retake the city last October, and it has driven the militants from all but a handful of neighborhoods.

Meanwhile, Syrian troops and allied militias met up with Iraqi forces at one crossing point along their shared border Sunday for the first time in years, in a step described as a major achievement by the Syrian military in their fight against Islamic State.

The meeting with Iraqi forces reported by pro-government media took place a day after Iraqi forces captured a border crossing point with Syria, al-Waleed, from Islamic State militants.