It said Syrian air defenses confronted the Israeli attacks, but without giving further details.
Israel then fired ground-to-ground rockets from the Israeli-occupied Golan Heights, but the Syrian defences brought the missiles down, the Syrian army said.
The reported attacks targeted Syrian military sites located in the al-Qutaifa area near Damascus.
"They are particularly vulnerable as they were displaced before, and they are fleeing into areas that are extremely packed - full to capacity - and struggling to cope particularly now with the weather", one of the officials said.
Some residents blame the Islamic State group for such attacks, although the group has no open presence in the province.
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Furthermore, the letter asserts that the attack allegedly conducted by Israel violates United Nations resolutions and would not have been possible without U.S. support.
For its part, Israel's Haaretz newspaper reported citing some sources in the Syrian opposition that the target was a weapons depot.
The three countries agreed previous year to establish a "de-escalation zone" in the opposition-held Idlib province and surrounding region, which borders Turkey, but Syrian forces have since launched an offensive in the area.
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The Britain-based Syrian Observatory for Human Rights on Monday gave a higher death toll, saying 34 people were killed, including 18 civilians.
The state-affiliated Al-Ikhbariya TV said government forces took Sinjar on Sunday.
Syrian media reports claimed Tuesday that the Israeli air force launched strikes targeting military outposts belonging to Syrian president Bashar Al-Assad's regime forces northeast of Damascus. The ministry said three of the armed drones landed outside the base and others detonated when they crashed, while seven drones were shot down.
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