UN chief Ban Ki-moon called Monday on all parties in the Arab-Israeli conflict to exercise "maximum restraint" and expressed "deep concern" about the shooting on the Golan Heights.
"The secretary-general regrets the loss of life, and extends his condolences to the families of the victims," said statement by Ban's spokesman.
"He condemns the use of violence and all actions intended to provoke violence."
The remarks came after Israeli troops opened fire on Sunday as protesters from Syria stormed a ceasefire line in the occupied Golan Heights, with Damascus saying 23 demonstrators were killed.
Hundreds of protesters rushed the ceasefire line, cutting through barbed wire as they tried to enter the territory in a repeat of demonstrations last month that saw thousands mass along Israel's north.
Similar protests were held in the West Bank and in the Gaza Strip.
In Majdal Shams, on the Golan, Israeli troops opened fire as demonstrators sought to push through the mined ceasefire line, which had been reinforced with several rows of barbed wire blocking access to a fence.
The UN spokesman said the United Nations Disengagement Observer Force (UNDOF) on the Golan was seeking to confirm facts and help calm the volatile situation in the area.
Ban has been following the events "with deep concern," the spokesman added.
"The events of today and of 15 May on the Golan put the long-held cease-fire in jeopardy," the statement warned. "The Secretary-General calls for maximum restraint on all sides and strict observance of international humanitarian law to ensure protection of civilians."
On May 15, thousands of protesters massed on Israel's borders with Syria, Lebanon and Gaza, trying to force their way across on the anniversary of Israel's creation.
Israeli fire left six demonstrators dead on the Lebanese side of the border and four dead on Syria's side.
Ban also reminded Syrian authorities of their obligation to protect UNDOF personnel and facilities, according to the statement.
The Golan was captured by Israel during the 1967 war and was later annexed by the Jewish state in a move that has not been recognised internationally.