Russia's Defence Ministry responded by suspending cooperation with the USA aimed at avoiding air incidents over Syria, where the Russian air force is bombing in support of President Bashar al-Assad's campaigns against rebels and IS.
The US military confirmed a US F-18 Super Hornet shot down a Syrian SU-22 on Sunday, after it dropped bombs near the US partner forces known as the Syrian Democratic Forces (SDF).
The Russian threat came just hours after the USA shot down a Syrian regime fighter jet that had dropped bombs on the US -allied Syrian Democratic Forces.
In Monday's statement, the Russian Defense Ministry said it considered the downing of the Syrian warplane "a cynical violation of the sovereignty" of Syria, and "a gross violation of worldwide law and, in fact, a military aggression against Syria".
The White House said on Monday that coalition forces fighting ISIS militants in Syria retained the right to self-defence as Russian Federation warned it viewed any planes flying in its area of operations as potential targets.
Russia's Defence Ministry announced that it was ending US-Russian co-operation in Syria that had been created to prevent a direct conflict between the great powers.
The incident was the latest skirmish between the US-led coalition and regime forces in the increasingly tense and crowded space in Syria's north and east.
The Syrian army said its warplane was on a mission against IS when it came under fire, according to state television.
The ministry also called on the USA military to provide a full account of why it made a decision to shoot down the Syrian SU-22.
But in a warning that the USA would protect its partners, Spicer said: "The Syrian regime and others in the region need to understand that we will retain the right of self-defense of coalition forces aligned against ISIS".
Russian Deputy Foreign Minister Sergei Ryabkov, in comments to Russian news agencies, compared the downing to "helping the terrorists that the U.S.is fighting against". The downing of the jet and Russia's response came as the US-led coalition and allied fighters battle to oust Daesh from its Syrian bastion Raqqa.
"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", the Pentagon said.
Moscow has previously threatened to scrap the deconfliction line, after an April 7 United States cruise missile strike on a Syrian regime airbase in retaliation for a suspected chemical weapons attack against civilians.