The drone was approaching a small military base at the Syrian town of Tanf that U.S., British and Norwegian special operations forces use as a staging ground to train and equip rebel groups fighting the Syrian government and Islamic State militants.
It is the first time in the Syrian conflict that the US-led coalition has shot down a Syrian jet.
In an indirect reference to Iranian-backed forces that have been gathering in the eastern desert region, the coalition statement cited a recent escalation of tensions and said it would not "tolerate any hostile intent and action of pro-regime forces".
Last week, another Iranian-made drone flown by pro-regime forces was shot down after it dropped munitions close to USA and partner forces.
Tanf is the town on Syrian border with Jordan where United States troops are training Syrian rebels, officially described as "partner ground forces". On June 8, the coalition also shut down a pro-regime drone.
On Sunday, June 18, the US F/A-18 Super Hornet shot down the Syrian aircraft, explaining its actions by the fact that the Su-22 dropped bombs on the US-backed Syrian Democratic Forces in the city of Raqqa, Syria.
U.S.' downing of the Iranian drone came on the same day when Australia announced it is temporarily suspending airstrikes by its forces in Syria after a threat from Russian Federation. However, American military officials rushed to the situation, saying they hoped Russian Federation to be persuaded to keep using the hotline.
"It's utterly unlawful. There is neither such a decision of the Security Council, nor a request by the legitimate authorities of the Syrian Arab Republic as a sovereign state", Deputy Foreign Minister Mikhail Bogdanovwas quoted as saying.
The SDF now control four neighbourhoods in the city, and on Tuesday also advanced along its southern outskirts, moving closer to completely encircling Raqa. But for now, they have stopped operations over Syria, "as a precautionary measure".
The last time Russian Federation threatened to cut off the deconfliction line was in April, when the USA launched missiles at a Syrian airbase in what ultimately amounted to a warning shot in retaliation for Assad's continued use of chemical weapons.
Davis noted Monday that most of the coalition's air operations occur east of the Euphrates, where ISIS has a larger presence, and that the USA has not seen behavior from Russian Federation that would "cause us concern".
On June 9, despite the series of engagements with USA forces at Al-Tanaf, the regime skirted around the base to arrive at the Iraqi border for the first time since 2015.
It said the fighters were trying to move out from Raqa towards Palmyra.