United Nations Secretary-General Antonio Guterres has called for an immediate de-escalation in Syria.
An Israeli F-16 fighter jet was shot down by Syrian air defences yesterday.
The pilots survived, but it was the first time Israel had lost a warplane in battle since 1982.
The strikes began with Israel shooting down what it described as an Iranian drone that had entered its airspace from Syria - calling it an "attack".
Iran denied the allegations regarding the drone and said Syria had the right to defend itself against Israeli attacks.
Mr Guterres is "following closely the alarming military escalation throughout Syria and the dangerous spillover across its borders," UN spokesman Stephane Dujarric said in a statement.
Mr Guterres stressed that all concerned in Syria and in the region must abide by international law.
"He calls on all to work for an immediate and unconditional de-escalation of violence and exercise restraint," Mr Dujarric said.
It was the most serious confrontation between Iran and Israel since Syria's war began in 2011 and came amid growing alarm over Syrian government offensives against rebel-held Eastern Ghouta and Idlib.
The Syrian people are suffering "though one of the most violent periods in nearly seven years of conflict," said the UN statement.
"Over 1,000 civilian casualties from airstrikes were reported in the first week of February alone."
Mr Guterres urged the parties to move quickly toward a political solution to end the war.
Diplomats have said there were no immediate plans to convene a council meeting despite the sharp rise in tensions.
The council is due to discuss the crisis in Syria on Wednesday.
Israeli Prime Minister Benjamin Netanyahu said that air strikes in Syria yesterday were a "heavy blow" to Iranian and Syrian forces in the war-torn country.
"We inflicted on Saturday a heavy blow to Iranian and Syrian forces," he said at the start of a cabinet meeting, referring to major Israeli air raids in Syria.
"We made clear to everyone that our rules of engagement will not change in any way. We will continue to harm anyone who tries to harm us. This was our policy and this will remain our policy."
Israel said its raids were against both Syrian and Iranian targets in Syria.
