JERUSALEM — Israel's military chief issued a stern warning to Bashar Assad on Tuesday, saying the Syrian leader would "bear the consequences" of any more attacks on Israeli forces near the Syrian border.

Lt. Gen. Benny Gantz issued his threat hours after an Israeli jeep came under fire during a patrol in the Israeli-controlled Golan Heights.

Syria claimed it destroyed an Israeli vehicle that crossed the cease-fire line in the Golan Heights overnight. The Israeli military said the vehicle suffered light damage. It said that the Israeli troops reported a "direct hit" from the return fire but provided no further details.

It was the latest in a string of incidents in which gunfire and mortar shells have struck the Golan in recent months. Israel believes that most of the fire has been spillover from the Syrian civil war, but that several cases, including Tuesday's were intentional.

That was bolstered by the fact that it was the first time the Syrian army has acknowledged firing at Israeli troops across the frontier in what appeared to be an attempt by Assad's regime to project toughness following three Israeli airstrikes near Damascus this year.

"Assad encourages and directs the widening of different operations against Israel, including the Golan Heights," Gantz told a conference at the University of Haifa.

He said in Tuesday's incident, the Israeli patrol was targeted several times by a "clearly marked Syrian position." He rejected Syrian claims that the vehicle had veered into Syrian territory.

"We will not allow the Golan Heights to become a comfortable space for Assad to operate from," Gantz said. "If he deteriorates (the situation on) the Golan Heights, he will have to bear the consequences."

Israel has warily watched the Syrian civil war, fearing the more than two-year-old conflict could spill across its borders.

Israel is concerned that Assad, in a bid of desperation, will try to escalate tensions on the border to draw in Israel and divert attention away from his struggles against rebel groups seeking his ouster. Israel also fears that Assad's sophisticated weapons could be transferred to Iranian-backed Hezbollah militants in Lebanon or fall into the hands of the rebels, including Islamic extremists connected to al-Qaida who are among their ranks who Israel believes will turn their attention to the Jewish state if they topple Assad.

Tensions have been rising between Israel and Syria in recent weeks, particularly following the airstrikes, which targeted alleged Syrian arms shipments bound for Hezbollah. Israel has not confirmed carrying out the attacks.

The strikes marked a sharp escalation of Israel's involvement in the Syrian civil war and raised fears that the conflict could turn into a full-fledged regional war.

Syria vowed to retaliate and Assad said Syria is "capable of facing Israel" and would not accept violations of its sovereignty. Firing at an Israeli target seems to be in line with the tougher rhetoric that followed the airstrikes.

Gantz visited the area after the incident and told soldiers stationed there and told them to "stay alert during these challenging times."