Israel faced the prospect of stepped-up military action on two fronts Monday as rockets fired from Gaza hit southern communities for the third straight day, and the army said it shelled a Syrian artillery battery after a stray shell landed near one of its posts in the Golan Heights.

The attack on the mobile artillery battery was the first time that Israeli forces had engaged Syrian troops across the Golan frontier since the 1973 Middle East war, and it ratcheted up tensions across a cease-fire line that has been quiet for decades.

On Sunday, the Israeli army said it fired a guided antitank missile into Syria as a warning after the landing of another errant shell that had been fired in fighting between Syrian troops and rebels. The Israeli responses followed several recent incidents in which stray munitions from the clashes in Syria had fallen in Israeli-held territory.

The renewed firing Monday heightened concerns that the Syrian conflict could draw in Israeli forces on the Golan Heights, a strategic plateau taken by Israel from Syria in the 1967 Six-Day War. The fighting in Syria has led to sporadic clashes on the country’s borders with Lebanon, Turkey and Jordan, raising fears that it could trigger wider regional conflict.

On Monday, Syrian jets bombed a rebel-held town along the Turkish border, killing more than a dozen people. Also Monday, a new umbrella organization for Syrian opposition groups was recognized by the six-nation Gulf Cooperation Council, the first formal endorsement the group has received.

An Israeli army statement on Monday’s Golan incident said that a shell fired “as part of the internal conflict inside Syria” landed harmlessly in an open area near an army outpost in the central Golan Heights — the same post hit by a stray mortar shell Sunday.

Israeli troops responded by firing “tank shells toward the source of the fire, confirming direct hits,” the statement said. Military officials said that the tank fire hit a Syrian mobile artillery unit and that there was no response from Syrian forces.

Syria did not comment on the incident, and it was not reported on state news broadcasts.

Eyal Zisser, an expert on Syria at Tel Aviv University, said that despite the flare-up, neither Israel nor the embattled Syrian government had an interest in widening the hostilities. “It’s not something that either side wants to get into,” Zisser said. “It’s a very local and measured incident.”

Defense Minister Ehud Barak said Sunday that the army had been ordered to prevent the fighting in Syria from spilling over the Golan frontier.

Rising public clamor

Top government and military officials seemed more preoccupied Monday with the rocket attacks in the south. Prime Minister Benjamin Netanyahu conferred with Barak and the army chief of staff to discuss possible responses that could address a rising public clamor for action without provoking an international outcry and rupturing delicate relations with Egypt, which has mediated between Israel and Hamas, the Islamist group that rules the Gaza Strip.

“We will take whatever action is necessary to put a stop to this,” Netanyahu told a gathering of foreign ambassadors he summoned to the southern city of Ashkelon, one of the targets of the rocket strikes. “It’s our right to defend our people, and this is what we shall do.”

The army said the number of rocket and mortar attacks from Gaza fell to 12 on Monday, compared with 75 the previous day. Nonetheless, the continued rocket strikes unsettled Israelis across a broad swath of towns and farming communities, where periodic alarms sent people running to shelters and several homes were damaged.

Militants in Gaza began launching the rockets Saturday after four Palestinians were killed and about two dozen more were wounded by Israeli shelling in response to a border attack that wounded four soldiers.

Limited options in Gaza

The continuing fire from Gaza set off a round of debate and speculation in Israel about what military action might be taken to halt the rocket attacks. Commentators raised the possibility of targeting Hamas leaders in Gaza, cutting off supplies to the territory or even a ground assault.

But analysts said that despite the tough talk about a decisive response, Israel’s options in Gaza were limited. “Israel fears a direct confrontation with the new regime in Egypt and it knows that neither the United States nor Europe will tolerate a large-scale military operation this time around,” wrote Amos Harel, the military correspondent for the Haaretz newspaper, in a joint column with Avi Issacharoff, the paper’s reporter on Palestinian affairs.

Israel launched a devastating offensive against Hamas in Gaza nearly four years ago in an effort to halt rocket fire, and the group has since largely stopped firing at Israel, though small militant organizations have continued their attacks, often after Israeli drone strikes targeting their members.

After a meeting between Hamas leaders and representatives of other militant factions in Gaza on Monday night, the factions indicated that they would be prepared to hold their fire if Israel stopped its attacks in Gaza.

“The ball is in Israel’s court,” said Khalid al-Batsh, a leader of Islamic Jihad. “The resistance factions will observe Israel’s actions on the ground and will act accordingly.”