Israel captured the Golan Heights, a strategic plateau, from Syria during a 1967 Middle East war. The 400-square-km (155-square-mile) zone is a so-called "area of separation" where Syrian military forces are not allowed under a 1973 ceasefire formalized in 1974. Israel and Syria are still technically at war.
The zone has been largely quiet since the ceasefire. But on Saturday an Israeli military spokeswoman said three Syrian tanks had entered the area and Israeli media said the tanks were involved in the fighting with rebels.
"The tanks remain in this area. Just today, gunfire from the Syrian side of the border struck an Israeli patrol," Israeli UN Ambassador Ron Prosor wrote to the Security Council in a letter dated on Monday and released on Tuesday.
"The international community and the Security Council should address this alarming development without delay to prevent further escalation," he wrote.
A revolt by Syrians against President Bashar al-Assad began as peaceful rallies calling for more freedoms and democracy but turned into an armed struggle after the military cracked down on protesters.
Diplomatic intervention has been fruitless because major world and regional powers cannot agree over how to end the conflict. It has killed about 32,000 people, making it the bloodiest of Arab uprisings that have ousted entrenched leaders in Tunisia, Egypt, Libya and Yemen since early last year.
Israel said Syrian tanks entering the Golan Heights represented "a dangerous escalation that could have far-reaching implications for the security and stability of our region."
UN Secretary-General Ban Ki-moon's spokesman Martin Nesirky said on Tuesday there had been sporadic fighting between Syrian troops and the opposition in the Golan Heights, with the Syrian army using mortar shells and tank rounds, some of which landed across the ceasefire line in Israeli-occupied territory.
"The presence of military personnel and the military operations in the area of separation is a grave violation of the 1974 Agreement on Disengagement between Israeli and Syrian forces," Nesirky told reporters.
"UNDOF (the UN peacekeeping mission) reported that the situation today is relatively quiet, but has not observed the battle tanks leaving," he said. "The UNDOF Force Commander continues to liaise with Syrian authorities and the Israel Defense Forces (IDF) to prevent an escalation of tension."