The Israel Defence Forces (IDF) immediately refuted the report, saying a Syrian anti-aircraft battery had shot at its aircraft but missed their target.
"Early this morning, two missiles were launched from Syria after the IAF targeted Syrian artillery positions," a spokesperson said. "IDF aircraft were not harmed."
The Israeli Air Force said Syrian troops used surface-to-air missiles in the attempt but that it “at no point” compromised pilot safety.
Bashar al-Assad's defence ministry previously issued a conflicting statement on Tuesday morning saying a fighter jet and drone were downed in Quneitra Governorate at 1am local time.
Officials claimed they were responding to “naked aggression [by the] Zionist enemy, supporting armed terrorist groups in a desperate attempt to raise morale that collapsed after heavy losses incurred in the Quneitra region”.
Quneitra borders Israel, Jordan and Lebanon and includes the disputed Golan Heights, which are partly occupied by Israel after being fought over in successive wars.
Much of the region was seized by rebels in 2014 after battles with the Syrian Arab Army and remains split between government and opposition control amid continued fighting.
Tuesday's dispute came hours after Israel announced its fighter jets had struck artillery positions manned by Syrian regime troops after a mortar landed in the occupied Golan Heights.
The incident was the fifth since last week in which fighting in Syria has spilled over into Israeli-occupied territory, and the first since a fragile truce brokered by the US and Russia came into effect.
The ceasefire came into force at sunset on Monday but Isis and the formerly al-Qaeda linked Jabhat al-Nusra group were excluded, while other rebel factions have refused to commit.
Despite his forces being part of the truce, President Assad vowed to take back the country from "terrorists" - a term used to describe all opposition groups.
Israel has largely remained on the sidelines of the fighting along its border, but has carried out reprisals on Syrian positions when errant fire has previously landed in Israel.
The IDF is also widely believed to have carried out airstrikes on arms shipments destined for the Lebanese militant group Hezbollah, a close ally of Assad.
Israel captured the Golan Heights from Syria in the Six Day War of 1967, before Syrian forces led an unsuccessful counter-offensive in 1973, and Israel effectively annexed the vast majority of the occupied territory in 1981.
The United Nations Disengagement Observer Force (UNDOF) was set up to monitor a ceasefire established in the region but fighting between the Syrian regime and rebels has frequently spilled over into the demilitarised area since 2012, sparking Israeli air strikes in Syrian territory.
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