The confrontation fueled new fears that the Syrian civil war could drag Israel into the violence, a scenario with grave consequences for the region. The fighting has already spilled into Lebanon, Jordan and Turkey.
"We are closely monitoring what is happening and will respond appropriately. We will not allow our borders to be violated or our citizens to be fired upon," Prime Minister Benjamin Netanyahu said Monday in a speech to foreign ambassadors.
While officials believe President Bashar Assad has no interest in picking a fight with Israel, they fear the embattled Syrian leader may try to draw Israel into the fighting in a bout of desperation. Israeli officials believe it is only a matter of time before Syrian rebels topple the longtime leader.
The conflict has already spilled over into several of Syria's other neighbors -- whether in direct violence or in the flood of refugees fleeing the bloodshed. More than 36,000 Syrians have been killed in the fighting, according to estimates by anti-Assad activists.
On Monday, a Syrian fighter jet bombed a rebel-held area hugging the border with Turkey three times, killing 15 to 20 people, according to a Turkish official. Separately, eight wounded Syrians died in Turkey, the official said, speaking on condition of anonymity because he was not authorized to brief the media.
Potential Israeli involvement in Syria could be far more explosive. The bitter enemies both possess air forces, tanks and significant arsenals of missiles and other weapons.
Although the Israeli military is more modern and powerful, Syria has a collection of chemical weapons that could wreak havoc if deployed. Fighting between the countries could also drag in Syria's close ally, the Lebanese guerrilla group Hezbollah, or Islamic militant groups in the Gaza Strip on Israel's southern flank.
Israeli political scientist Dore Gold, an informal adviser to Netanyahu, said neither Israel nor Syria has any interest in escalating the fighting.
"I see no indication of Assad wanting to draw Israel in. But if violence comes from the Syrian army, or even forces operating in Syria that are affiliated with al-Qaida, Israel has to do what is necessary to make sure there's no spillover into Israeli territory," he said.
He described Israel's reaction Monday as a "carefully calibrated response."
"On the one hand, it shows Israel's determination to protect its civilians, and at the same time, it indicates it doesn't want to get drawn in," he said.
Israel has warily watched the fighting in Syria for months, carefully trying to avoid any involvement. It has found itself in a difficult position as the fighting rages near the frontier with the Golan Heights, a strategic plateau it captured from Syria in 1967 and later annexed.
A number of mortar shells have landed in the Golan in the past week. Early this month, Syrian tanks accidentally crossed into a buffer zone along the frontier for the first time in nearly 40 years.
Israel responded for the first time Sunday, firing what it called a "warning shot" into Syria after a mortar shell landed near an Israeli military post. Israel also warned of a tougher response if the attacks persisted.
In Monday's incident, the military said it reported "direct hits" on a mobile artillery launcher after another shell struck the Golan. It would not say whether the launcher belonged to the Syrian army, saying only it had targeted the "source of fire."
The Israeli military believes the mortar fire is spillover from internal fighting in Syria and not aimed at Israel. But officials say they are beginning to question that assessment after repeated breaches of the frontier.
The incident began when Syrian military units were shelling gunmen in the twin Syrian villages of Bariqa and Bir Ajam, only several hundred meters (yards) from Israeli-held territory. An Associated Press photographer on the Golan side saw gunmen, presumably rebels, running as explosions shook the village from the shelling by Syrian army mobile artillery visible about a mile away (2 kilometers).
The rebels fired back with automatic weapons and then fled, running toward the Golan border and taking refuge under some trees. A few minutes later, the rebels made their way back to the village.
Bursts of artillery fire from the Syrian forces could be heard every few minutes, and about a half-hour later, the Syrian shell struck the Golan, making a loud whistling sound before impact less than 100 meters (yards) from an Israeli position. Israeli forces quickly opened fire, and a plume of smoke billowed from one of the tanks' guns.
The Syrian Observatory for Human Rights, a Britain-based, anti-Assad group that relies on a network of activists on the ground in Syria, confirmed fighting in the area. It said three rebel fighters were killed Monday in clashes with the Syrian army in Bir Ajam.
The state-run news agency SANA has not reported on the fighting in the area or the clash with Israel.
Israel has little love for Assad, who has provided refuge and support to Israel's bitterest enemies through the years. But he and his father before him have kept the frontier quiet for nearly four decades, providing a rare source of stability in the volatile region.
Israel fears Assad may stage an attack if he fears his days are numbered. It also worries that Syria's chemical weapons could fall into the hands of Hezbollah or other anti-Israel militants. There also are concerns that al-Qaida-linked groups battling Assad could turn their focus toward Israel, or sectarian warfare might send refugees streaming into Israel.
The aftermath of Egypt's revolution has provided Israel with reason to worry about its frontier region with Syria: Egypt's Sinai desert on Israel's southern border has turned even more lawless since longtime Egyptian President Hosni Mubarak was ousted in February 2011. Islamic militants have frequently exploited the situation there to attack Israel.
The Golan frictions were a potent reminder of how easily the Syrian civil war could explode into a wider regional conflagration.
Syrian airstrikes on Ras al-Ayn, on the country's northern border, once again raised tensions with Turkey. Regime forces and rebels have been battling for days over the town, which is practically adjacent to the border.
Last week, Syrian rebels overran three security compounds in Ras al-Ayn and took control of the town, located in Syria's predominantly Kurdish, oil-producing northeastern province of al-Hasaka. A surge of 11,000 Syrians escaped into Turkey on Friday following the fighting at Ras al-Ayn.
Turkish Foreign Minister Ahmet Davutoglu, speaking to reporters in Rome, said Ankara had formally protested the bombings near the border, saying the attacks were endangering Turkey's security, state-run TRT television reported. He said Turkey had also reported the incident to NATO allies and to the U.N. Security Council.
Davutoglu said the bombings showed that the Syrian regime was attacking its people without making a distinction between "civilians or military units," according to TRT.
Federman reported from Jerusalem. Associated Press Lauren E. Bohn in Jerusalem, Aron Heller in Ashkelon, Israel, Suzan Frazer in Ankara, Turkey, and Mehmet Guzel in Ceylanpinar, Turkey, contributed to this report.
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