Hundreds of protesters tried to cut through a line of barbed wire and head into the Golan Heights, as happened during demonstrations last month.
Similar protests were held in the West Bank and Gaza. They were organised to mark the anniversary of the 1967 six-day war, when Israel seized the Golan Heights and the Palestinian Territories.
US President Barack Obama recently called on Israel to accept a Palestinian state within the 1967 borders but advised the Palestinians to drop an attempt to gain UN recognition of a state in September.
“Despite numerous warnings, both verbal and later warning shots in the air, dozens of Syrians continue to approach the border and IDF [Israel Defence Forces] forces were left with no choice but to open fire towards the feet of protesters in efforts to deter further actions,” an army spokesperson told the AFP news agency.
As well as the four dead, one of whom was a child,13 people were wounded, Syrian TV said.
An AFP photographer saw at least 20 people with injuries, while the Israeli military said it was aware of 12 casualties.
In Lebanon, Palestinian refugees on Sunday staged a day of mourning but the Lebanese army banned any gatherings at the border with Israel, saying that they wished to avoid a repetition of last month's violence.
Several thousand people demonstrated against the occupation of the Palestinian Territories in Tel Aviv on Saturday.