The strikes are the first time Iran has fired missiles at another country in three decades and represent a major escalation of Iran's role in the war in Syria.
Gen. Joseph Dunford, Chairman of the Joint Chiefs of Staff, said he was confident that there's still a means of communicating with the Russians, according to Fox News.
Rhetoric between the United States and Russian Federation has escalated since an American jet shot down a Syrian plane on Sunday.
Moscow is terminating its communication channel with the United States under a memorandum for preventing incidents in Syria's skies, as a outcome for the U.S. downing a Syrian Su-22 plane, Russia's Defense Ministry reported on Monday.
Russian Federation also said it was halting communications with the US aimed at preventing such incidents.
The Russian defense ministry said in a statement on Monday that it was suspending the deal after the USA military confirmed that it downed a Syrian Air Force fighter jet on Sunday after it dropped bombs near US partner forces.
Russia's decision came after the US confirmed it shot down a Syrian Su-22 fighter bomber Sunday. The attack began after the pro-Syrian forces attack a US -backed rebel group called the Syrian Democratic Forces southwest of Raqqa.
Russia said its warplanes were flying over Syria at the time of the shootdown and the US failed to use the existing deconfliction channel between USA military officers at al-Udeid air base in Qatar and Russian officers at Hemeimeem air base.
In a statement issued Tuesday, the Australian Department of Defence said: "As a precautionary measure, Australian Defence Force strike operations into Syria have temporarily ceased".
The Russian defense ministry said on Monday that it will treat any aircraft in Syria west of the Euphrates river as a target. The Syrians assert that the plane attacked the ISIS terrorist group.
The immediate effect on the US -led campaign against IS is unclear. Russian Federation said it will now treat any aircraft or drones as threats if they operate in any areas west of Euphrates.
The U.S. and its coalition partners fly combat and support missions daily out of several bases in the Middle East, including in Qatar and Turkey.
Both sides are battling the Islamic State group, with SDF fighters focusing on their march into the northern city of Raqqa, which the extremist group has declared to be its capital.
Officials called the drones actions "unacceptable" and said the US shot it down before it was too late to protect the troops on the ground.
Russian Federation has been a staunch supporter of Syria's beleaguered President Bashar Assad and has been providing an air cover for his offensive against IS since 2015.
"The worst thing any of us could do right now is address this with hyperbole", Dunford said.
The U.S. spy plane was in worldwide airspace when the Russian jet closed in for an intercept.