On Sunday, Prime Minister Benjamin Netanyahu told his Cabinet that Israel is "closely monitoring" the border with Syria and is "ready for any development."
U.N. Secretary-General Ban Ki-moon said in a statement from his New York office that the shelling was reported in the U.N.-monitored zone between Israel and Syria, but no injuries to civilians or U.N. personnel were reported.
Ban called "for the utmost restraint" and urged Syria and Israel to uphold their cease-fire agreement and halt any exchange of fire.
The violence in Syria has killed more than 36,000 people in the uprising that began in March 2011. Hundreds of thousands have fled the fighting into neighboring Turkey, Jordan, Lebanon and Iraq. Another 11,000 escaped Friday into Turkey following the surge of fighting at Ras al-Ayn.
Ismail Aslan, the mayor of the nearby Turkish town of Ceylanpinar, said the number of refugees had slowed significantly Sunday. But Turkish soldiers at the border turned back some of the refugees who had arrived late last week and wanted to return to Ras al-Ayn, saying the area was not secure.
Activists reported clashes and shelling in different parts of Syria, killing almost 60 people, nearly two-thirds of them civilians.
The violence spread in most provinces around the country from Diaraa and Quneitra in the south to Idlib and Aleppo in the north to Homs and Hama in the center and Deir el-Zour in the east.
There also was fighting in Damascus and its suburbs, mostly in the capital's southern neighborhood of Tadamon.
In Qatar, Syrian activists said anti-government groups had reached a preliminary deal to form a new opposition leadership under pressure from the international community.
Ali Sadr el-Din Bayanouni, a former Syrian Muslim Brotherhood leader, said a broad agreement has been struck among the opposition factions to form a new group called the Syrian National Coalition for Opposition and Revolutionary Forces.