Downing an Israeli fighter jet by Syrian fire marks one of the most serious escalations in the region, BBC's Middle East correspondent Tom Bateman said.
During the attack, multiple anti-aircraft missiles were fired at Israeli Air Forces aircraft, said the Israeli army.
Israel attacked multiple ground targets in Syria using airstrikes early Saturday morning.
"IDF [Israel Defence Forces] has targeted the Iranian control systems in Syria that sent the #UAV into Israeli airspace".
Israel has repeatedly warned in recent weeks against the presence of Iranian forces in neighbouring Syria.
"This is the most significant attack on the Syrian air defense since the Operation Peace for Galilee [1982 Lebanon War]..." Qasemi went on to say, "Iran only provides military advice to Syria based on the request of the country's legitimate government".
Russian Federation views Iran as a key player in resolving the crisis in Syria, but with today's events, the message Israel passed to Tehran via Moscow was either not received or was ignored by the Islamic Republic, which is investing serious efforts in how Syria will look once the disastrous war ends.
The ministry added: "We urge all parties involved to exercise restraint and to avoid any actions that could lead to an even greater complication of the situation".
US Secretary of State Rex Tillerson is expected to visit the region in the coming week to discuss Syria and other issues, and is scheduled to visit Jordan, Turkey, Lebanon and other countries.
Russian Federation backs the Assad and maintains a large military presence in the country.
The Israeli military said Saturday it shot down an Iranian drone that infiltrated the country and struck Iranian targets in that launched it. According to the Israeli military, the confrontation began with the drone entering its airspace before being intercepted by a combat helicopter.
Conricus declined to give details on the drone's presumed mission or whether it was armed.
In March of previous year Israel, used its Arrow advanced missile defense system for the first time in a combat situation after Israeli jets, also operating near Palmyra, were targeted.
Over the past years, Israel has frequently attacked targets in Syria, often claiming that it hit positions or convoys belonging to Iran.
"We are willing, prepared and capable to exact a heavy price from anyone that attacks us, however, we are not looking to escalate the situation", army said in a statement. "We have to be careful about how Syria will look like when it is controlled by Iran".
Such "terrorist action by Israel would be met with a severe and serious response", announced the military alliance fighting in support of the Syrian regime in a statement following the downing of the jet.
The regime said it intercepted the missiles and destroyed a lot of them, according to SANA.
Despite the escalation on the northern border, some 100,000 people visited national parks throughout the country on Saturday, including in the north, the Israel Nature and Parks Authority said.
According to Kuperwasser, Moscow is "being used by the Iranians", securing Assad regime bases while Tehran continues to strengthen their hold in Syria.
Syrian President Bashar al-Assad's regime recently intensified airstrikes on rebel-held areas such as the northwestern Idlib province, prompting tens of thousands of civilians to flee their homes, according to United Nations officials.