The military said the trio were apprehended some 20 kilometres (12 miles) inside Israel near an army base, while police distributed pictures of hand grenades, knives and wire cutters found on them.

"We don't know who sent them and what their purpose was," an army spokeswoman told AFP.

Defence Minister Avigdor Lieberman, on an inspection tour of southern Israel near the Gaza border, said he had ordered a probe and expected the results on Thursday.

The detentions come as Israel braces for the annual Palestinian Land Day protests, commemorating the killing of six unarmed Arab protesters in Israel in 1976, set to begin on Friday in Gaza and the West Bank.

This year's demonstrations appear especially combustible as Palestinian anger is already high over US President Donald Trump's decision in December to recognise Jerusalem as Israel's capital.

Gazans are being called to march en masse toward the Israeli border fence that seals off the coastal territory from the Jewish state.

There have already been several incidents along the border in recent days.

A number of Palestinians on Saturday breached the frontier and tried to torch heavy equipment, following which Israeli jets attacked positions of Hamas, the Islamist group that controls Gaza.

A day later gunfire from Gaza set off Israel's Iron Dome air defence system and in response an army tank fired at a Hamas position.

Israeli Construction Minister Yoav Gallant, a member of the security cabinet, warned Tuesday against attempts to breach the southern border as part of the Land Day events.

"The temperature is literally rising," he said. "The motivation is greater than in the past."

"If they want to behave peacefully inside the Gaza Strip, this is their own business," Gallant said.

"But if we see the motivation to cross the border, we will not act only in the last second when thousands of people are destroying the fence."