"The Islamic Revolution Guards Corps warns the takfiri terrorists and their supporters in the region and outside the region that if they repeat their evil measures against the Iranian nation, the IRGC's revolutionary rage and flames of revenge will hit those responsible for such actions and will send criminals to hell", the statement said.
Iran backs Syrian President Bashar al-Assad in his fight against anti-government rebel groups and ISIS, which is primarily based in the Syrian city of Raqqa.
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It appeared to be Iran's first missile attack overseas in over 15 years and its first in the Syrian conflict, in which it has provided crucial support to Assad.
Earlier, Iran had implicitly suggested that the USA and Saudi Arabia, its chief regional foe, had insinuated the terrorist attacks in Tehran. Foreign Minister Mohammad Javad Zarif said the strikes highlight the benefits of Iran's missile program.
The attacks marked the the first time that ISIS, a Sunni Muslim group fighting Iranian-backed militias in Syria, has claimed responsibility for an attack in Iran.
The Guard said it fired six missiles in total from Kermanshah and also from Iran's Kurdistan province into Syria's Deir el-Zour province, where IS has been trying to fortify its positions in the face of a US -led coalition onslaught. The Syrian army said the warplane was on a mission against Islamic State militants when it was shot down.
Saudi Arabia, the U.A.E., Bahrain and Egypt earlier this month cut diplomatic relations with Qatar, partly over its ties with Iran, plunging the region into its biggest crisis in decades.
It is unclear whether the IRGC also coordinated with Iraq prior to launching the missiles into Iraqi airspace.
Israel is also concerned about Iran's missile launches and has deployed a multilayered missile-defense system.
Sharif said on Monday, however, that the missiles were not only aimed at sending a message to IS, but also to Riyadh and Washington.
Iranian officials meanwhile offered a series of threats of more strikes, including former Guard chief Gen. Mohsen Rezai.
The "flagrant aggression" highlights coordination between the USA and Islamic State and "reveals the evil intentions fo the U.S. in administering terrorism", the general command said in a statement carried by state-run SANA news agency.