JERUSALEM, April 8 (Reuters) - Israeli jets hit Syrian military targets on Sunday in response to rockets launched towards Israeli controlled territory overnight, Israel's military said, as violence flared again following cross-border exchanges of fire during the week.

State media in Syria reported explosions in the vicinity of the capital Damascus as Israel said its forces continued to hit Syrian territory after six rockets were fired overnight towards the Golan Heights.

Israel said artillery and drone strikes hit the rocket launchers and were followed by airstrikes against a Syrian army compound, military radar systems and artillery posts.

The Israeli military "sees the State of Syria responsible for all activities occurring within its territory and will not allow any attempts to violate Israeli sovereignty," the Israeli Defense Forces said in a statement.

The Syrian defence ministry said its air defences had responded to the Israeli attacks and intercepted some Israeli missiles. It said no casualties had been reported with only material damage caused by the strikes.

Sirens had sounded earlier near towns in the Golan Heights as rockets were launched from Syrian territory, but no damage or casualties were reported. Israel seized the Golan Heights in the 1967 Middle East war and annexed the 1,200-square-km (460-square-mile) territory in 1981, a move not recognised by most of the international community.

Only three of the rockets crossed into Israeli-controlled territory, with two falling on open ground and a third intercepted by air defence systems, the military said.

Lebanon-Based Al Mayadeen TV said the rocket salvoes were claimed by Al-Quds Brigades, the armed wing of the Iranian-backed Palestinian Islamic Jihad movement.

On Thursday, more than 30 rockets were fired towards Israel from southern Lebanon, drawing cross-border counterstrikes from Israel on sites linked to the Islamist movement Hamas in Lebanon and Gaza.

The cross-border exchanges came amid sharply increased tensions between Israel and Palestinian groups following Israeli police raids in recent days on Al-Aqsa mosque in Jerusalem, which caused outrage across the Arab world.

Israel said the operations were intended to dislodge groups of what police called extremists that had barricaded themselves into the mosque armed with firecrackers and stones.

But the raids, during the Muslim holy month of Ramadan, drew a furious reaction and concern even among Israel's U.S. allies, with mobile phone footage from inside the mosque showing police beating worshippers.

The site in Jerusalem's Old City, holy to both Muslims and Jews, who know it as Temple Mount, has been a longstanding flashpoint, notably over the issue of Jewish visitors defying a ban on non-Muslim prayer in the mosque compound.

Clashes there in 2021 helped set off a 10-day war between Israel and Hamas. The recent exchanges of cross-border fire have awakened memories of that conflict.

Despite fears of further violence around the mosque on Saturday, there were no reports of serious disturbances overnight.

In a separate incident, a Palestinian man was shot dead by Israeli forces during a confrontation in the occupied West Bank, Israel's military and the Palestinian health ministry said.