The general command called the action a "flagrant aggression" that affirmed the United States' "real stance in support of terrorism", according to Syrian Armed Forces.
The U.S. Navy shot down a Syrian government fighter jet in retaliation for dropping bombs on U.S. -backed rebels.
The U.S. military says it shot down a Syrian Air Force jet that dropped bombs near U.S. -backed forces in the fight against Islamic State militants in Iraq and Syria. The defence ministry also condemned the downing of the jet and said that the act was a violation of global law.
The Russian Defence Ministry said it was also scrapping a Syrian air safety agreement with Washington created to avoid collisions and risky incidents with immediate effect.
Russian Federation has threatened aircraft from the US -led coalition in Syrian-controlled airspace and suspended a hotline meant to avoid collisions in retaliation for the USA military shooting down a Syrian warplane.
Iran and Syria are determined to establish a "Shiite" supply corridor between Iran and Syria that would run directly through territory on the Iraq-Syria border that is now controlled by coalition forces based out of the At Tanf garrison.
The incident marks the fourth time within a month that the U.S. military has attacked pro-Syrian government forces, The Washington Post reported.
A senior military officer told The Canadian Press during a visit to the region in February that the Auroras and Polaris had flown between 20 and 30 missions over Syria in the previous few months.
He said the provocations by Syria's government and its allies were a potentially risky strategy. "If we're talking about an escalation in the tension, there could be some concern for the Canadians, absolutely".
A United States aircraft shot down a manned fighter jet of the Syrian government on Sunday, the Pentagon said in a statement.
Canada also has 200 special forces troops in northern Iraq, along with a helicopter detachment and a combat hospital.
US -backed opposition fighters said Assad's forces have been attacking them in the northern province of Raqqa and warned that if such attacks continue, the fighters will take action. But the US military said it would defend USA -backed forces when necessary.
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 incident was preceded by an attack by pro-government forces on some US -backed rebels nearby, and it was followed by a statement from Russian Federation that it would suspend cooperation with the USA over Syria and treat coalition aircraft as potential targets.
The U.S. move proves that Washington has redlines for the Syrian army to stay away from, as such areas including near the Iraqi borders and Raqqa are the share of the U.S. -backed forces.
The Pentagon noted that the United States military used a deconfliction channel to communicate with Russia, Syria's main ally, before downing the plane to prevent the incident from escalating.