Hezbollah said that an Israeli F-16 was shot down on Saturday marks the "start of a new strategic phase," in an official statement released on Saturday.
The comments come after multiple Israeli strikes on Syrian and Iranian targets in Syria, following a downing of an Iranian drone which entered Israeli airspace, and a downing of an Israeli F-16 by Syrian air defenses.
Hezbollah condemned Israeli aggression, stating that exploitation of Syrian airspace will be limited. "Today's developments mean the old equations have categorically ended," said the statement.
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Moscow also expressed serious concerns about the latest developments in Syria and called on the sides to exercise restraint and avoid an escalation of the situation, the Russian Foreign Ministry said on Saturday.
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"We urge all sides to exercise restraint and to avoid any actions that could lead to an even greater complication of the situation," the ministry said in a statement. "It is necessary to unconditionally respect the sovereignty and territorial integrity of Syria and other countries in the region."
Iran, meanwhile, issued its first official response to the events, with its Foreign Ministry rejecting as "ridiculous" reports that Israel had intercepted an Iranian drone launched from Syria.
"Reports of downing an Iranian drone flying over Israel and also Iran's involvement in attacking an Israeli jet are so ridiculous ... Iran only provides military advice to Syria," TV quoted Iran's Foreign Ministry spokesman Bahram Qasemi as saying.
Earlier on Saturday, the pro-Assad military alliance, which includes Iran and Hezbollah, warned Israel that any new act of what it called "terrorism" will be met with a "severe and serious response."
The statement said that Israel claims the drone entered Israeli airspace are "a lie," adding that the drones were being used to combat the Islamic State.
A senior official was quoted in the statement saying he does not believe matters will develop into a regional war.
Meanwhile, the deputy head of Iran's elite Revolutionary Guards Corps declined to comment on the drone incident, the semi-official Tasnim news agency reported.
"We cannot confirm this report on the drone because Israelis are liars ... if Syrians confirm it, Iran will confirm it as well," Brigadier General Hossein Salami said, according to Tasnim.
On Saturday, Israel targeted 12 sites around Damascus after an Israeli F-16 was downed. According to the Israeli army, Syrian anti-aircraft missiles targeted the jet after Israel responded to the infiltration of an Iranian drone with a strike in Syria.
The two F-16 pilots ejected as the plane went down in northern Israel. The pilots were taken to the hospital in stable condition. One of the pilots is in serious condition. Following the downing of the jet Israel responded with a fresh "large-scale strike" in Syria.
An Israeli military spokesman said that Syria and Iran are "playing with fire" and will pay a heavy price. The Prime Minister's Office has instructed cabinet ministers not to speak publicly about the events on the northern border.