Israel in deadliest Syria strikes this year
Stay tunned with 24 News HD Android App
The Syrian Observatory for Human Rights said an ammunition depot and several positions linked to Iran's military presence in Syria were among the targets.
"The Israeli enemy carried out an air assault at dawn... targeting several positions around Damascus," a military source was quoted as saying by the state news agency SANA.
"The investigation indicated that four soldiers were killed, three others injured and material damage noted."
The latest strike follows another near Damascus on April 14, without casualties, according to SANA.
The other four killed were not members of the Syrian military but belonged to Iran-backed militia, Observatory chief Rami Abdel Rahman said, adding he could not verify their nationality.
He said at least five separate sites were targeted in the latest Israeli raid.
AFP correspondents in the Syrian capital said they heard loud explosions.
Since the war broke out in Syria in 2011, Israel has carried out hundreds of air strikes inside the country, targeting government positions as well as allied Iran-backed forces and Shiite militant group Hezbollah.
The Israeli military has defended them as necessary to prevent its arch-foe Iran from gaining a foothold on its doorstep.
The conflict in Syria started with the brutal repression of peaceful protests and escalated to pull in foreign powers and global jihadists.
It has killed nearly 500,000 people and displaced half of the country's population.