* Israeli aircraft strike several Syrian targets
* Israel says won't tolerate attacks on troops
* Official Syria media silent (Adds Syrian army statement, paragraph 2)
By Jeffrey Heller
JERUSALEM, March 19 (Reuters) - Israel launched air strikes on Wednesday against Syrian military sites in response to a roadside bombing that wounded four of its soldiers, but both sides signalled they were not seeking further escalation.
The Syrian army, embroiled in a civil war, said one soldier was killed and seven were wounded in the air raids on three targets. Although Damascus condemned the Israeli attacks, it stopped short of any direct threat of retaliation and affirmed its focus on defeating insurgents.
Israel, by announcing the air raids, as opposed to its official silence about past strikes on arms from Syria believed destined for Lebanon's Hezbollah guerrillas, appeared intent on delivering a message of deterrence to President Bashar al-Assad.
"Our policy is clear. We hurt those who hurt us," Israeli Prime Minister Benjamin Netanyahu told his cabinet in public remarks.
"Syrian elements not only allowed but also cooperated in the attacks on our forces," he said, and by taking military action now the Jewish state wanted to ensure calm was re-established along its northern frontier.
The attack came less than a month after Hezbollah accused Israel of carrying out an air strike on one of its bases on the Lebanon-Syria border. It vowed at the time to respond.
In Tuesday's violence, a bomb was detonated near an Israeli patrol along a fence between the Israeli-occupied Golan Heights and the part of the strategic plateau under Syrian control. One of the four wounded soldiers was in critical condition.
Although suspicion in Israel fell on Hezbollah, Israeli leaders did not point a finger directly at the Shi'ite Muslim group, which is allied with Assad in battling a three-year-old rebellion against his rule led by Sunni Islamist insurgents.
While the Syrian army has a presence in the Golan, some areas are controlled by the rebels fighting to topple Assad, including al Qaeda-inspired militants hostile to the Jewish state. Israel has voiced concern that it will increasingly become a target during and after the Syrian conflict.
ISRAEL WARNS OF "HEAVY PRICE"
"We hold the Assad regime responsible for what happens in its territory and if it continues to collaborate with terrorists striving to hurt Israel, then we will keep on exacting a heavy price from it and make it regret its actions," Israeli Defence Minister Moshe Yaalon said.
Netanyahu, in his remarks to the cabinet, also alluded to Israeli air strikes against weapons shipments, saying Israel had taken action during the Syrian conflict to "thwart, as much as we can, the transfer of arms by sea, air and land".
But Amos Yadlin, a former chief of Israeli military intelligence, said there was "no desire for escalation" on Israel's part, noting the air force was capable of carrying out attacks far more dramatic than Wednesday's pre-dawn strikes.
The Israeli military said targets of the latest air strikes had included a Syrian military headquarters, a training facility and artillery batteries on the Syrian-held side of the Golan.
Occasional spillover violence on the Golan from the Syrian civil war has often drawn Israeli return fire against Syrian positions, ending what had previously been a stable ceasefire between the foes since the 1973 Middle East war.
"There is no spillover here," Yadlin told Army Radio, referring to the roadside bombing.
"When the other side changes the rules of the game, Israel has to make clear it carries a very high price. I think Assad understands the price," said Yadlin, who heads Tel Aviv University's Institute for National Security Studies.
Israel captured the Golan from Syria in 1967 and annexed it in a move not recognised abroad. The wounding of the soldiers on the strategic plateau marked Israel's worst casualties there since the start of Syria's conflict in 2011. (Additional reporting by Maayan Lubell; and Dan Williams in Jerusalem and Dominic Evans in Beirut)