Syria’s ally, Iran, also said there will be repercussions for the Jewish state over the attack.
In a letter to the UN Secretary-General, Syria stressed the country's "right to defend itself, its territory and sovereignty" and holding Israel and its supporters accountable.
"Israel and those who protect it at the Security Council are fully responsible for the repercussions of this aggression," the letter from Syria's Foreign Ministry said.
US officials said Israel launched a rare airstrike inside Syria on Wednesday. The target was a convoy believed to be carrying anti-aircraft weapons bound for Hezbollah, the powerful Lebanese militant group allied with Syria and Iran.
In Israel, a lawmaker close to hard-line Prime Minister Benjamin Netanyahu stopped short of confirming involvement in the strike. But he hinted that Israel could carry out similar missions in the future.
The attack has inflamed regional tensions already running high over Syria's 22-month-old civil war.
Israeli leaders in the days leading up to the airstrike had been publicly expressing concern that Syrian President Bashar Assad may be losing his grip on the country and its arsenal of conventional and nonconventional weapons.
The Syrian military denied there was any weapons convoy and said low-flying Israeli jets had crossed into their country over the Israeli-occupied Golan Heights to bomb a scientific research centre near Damascus.
It said the target was in the area of Jamraya, northwest of Damascus and about 15 kilometres (10 miles) from the Lebanese border.
Syrian Ambassador to Lebanon Ali Abdul-Karim Ali threatened retribution for the Israeli airstrike, saying Damascus "has the option and the capacity to surprise in retaliation”.
He told Hezbollah's al-Ahd news website that it was up to the relevant authorities to prepare the retaliation and choose the time and place.
The Syrian Foreign Ministry summoned Major-General Iqbal Singh Singha, the head of mission and force commander for United Nations Disengagement Observer Force (UNDOF) on the Golan Heights, to complain about the Israeli violation.
The force was established in 1974 following the disengagement of Israeli and Syrian forces in the area and has remained there since to maintain the ceasefire. Israel captured the Golan, a strategic plateau, from Syria in the 1967 Middle East war.
Hezbollah condemned the attack as "barbaric aggression" and said it "expresses full solidarity with Syria's command, Army and people."
The group did not mention any weapons convoy in the statement but said the strike aimed to prevent Arab and Muslim forces from developing their military capabilities.
In Iran, the semi-official Fars news agency quoted Deputy Foreign Minister Hossein Amir Abdollahian as saying the raid will have significant implications for Israel.
Iranian Foreign Minister Ali Akbar Salehi condemned the airstrike on state television, calling it a clear violation of Syrian sovereignty. Iran is Syria's strongest ally in the Middle East, and has provided Assad's government with military and political backing for years.
Russia, Syria's most important international ally, said this appeared to be an unprovoked attack on a sovereign nation. Moscow said it was taking urgent measures to clarify the situation in all its details.
A UN diplomat confirmed that the organization received a letter from the Syrian ambassador but said it did not contain a request for a Security Council meeting.
A UN statement said Secretary-General Ban Ki-moon expressed grave concern over reports of Israeli airstrikes on Syria but said the UN does not have details of the reported incident and cannot independently verify what happened.