Israel's army accused Syrian President Bashar Al-Assad's regime of "organising" Sunday's violence on the Golan Heights as a way to divert attention from pro-democracy protests sweeping his country.

"The Syrian authorities organised this violent incident in order to divert world opinion away from what is happening in their cities," army spokeswoman Avital Leibovitz told AFP.

Israeli troops wounded "dozens" of people when they opened fire at protesters from Syria forcing their way onto the disputed Golan Heights on Sunday, the military said.

The army said soldiers opened fire when "thousands of Syrian civilians breached the Israel-Syria border near the Israeli village of Majdal Shams."

But Leibovitz later clarified that although there were thousands of protesters, only dozens had managed to cross the frontier, in an incident she described as "very serious and violent."

"Thousands of protesters from the Syrian side of the border attacked our troops with stones and dozens of them entered into Israel," she said, toning down an army statement that "thousands" had crossed.

"Our forces unleashed warning shots to keep them back" from Israeli-annexed territory on the plateau which Israel seized from Syria in the 1967 Middle East war, Leibovitz said.

This was "a very serious and violent incident which threatens the security of the inhabitants of Israel and violates its territory," she said.

Meanwhile, Syria on Sunday lashed out at Israel for opening fire on protesters in the Golan Heights, south Lebanon and Gaza, warning that the Jewish state would bear full responsibility for its "criminal" actions.

"We firmly denounce the criminal Israeli actions against our people in the Golan Heights, Palestine and southern Lebanon that left several people dead and wounded," the foreign ministry said.

"Israel will have to bear full responsibility for its actions."