The shooting appeared to be an isolated incident and was unlikely to jeopardise the Egyptian-brokered cease-fire, which called for an end to Gaza rocket fire on Israel and Israeli air strikes on Gaza. The truce came after eight days of cross-border fighting, the bloodiest battle between Israel and Hamas in four years.
The Gaza Prime Minister, Ismail Haniyeh of Hamas, has urged militant factions to respect the cease-fire.
The man killed on Friday was part of a group of people who approached Israel's border fence with Gaza to pick up parts of an Israeli army jeep damaged in the fighting, said Gaza health official Adnan Abu Salmia. He said soldiers opened fire, killing one man and wounding nine.
Israel's military, citing a preliminary investigation, said there have been isolated attempts to infiltrate Israel from Gaza, and that warning shots were fired in the air when the group approached on Friday. The military said there was unrest along the border but did not elaborate.
In the past, Israeli troops enforced a no-go zone on the Gaza side of the frontier, firing on anyone approaching in an attempt to prevent infiltration attempts. Since the cease-fire, growing numbers of Gazans have entered the zone.
In Cairo, Egypt was set to hold separate talks Friday with Israeli and Hamas envoys on the next phase of the cease-fire, a new border deal for blockaded Gaza.
Hamas demands a lifting of all border restrictions, while Israel insists that Hamas must halt weapons smuggling to the territory.
In Israel, a poll showed that about half of Israelis think their government should have continued its military offensive against Hamas.
The independent Maagar Mohot poll released on Friday shows 49 per cent of respondents feel Israel should have kept going after squads that fire rockets into Israel. 31 per cent supported the government's decision to stop. 20 per cent had no opinion. 29 per cent thought Israel should have sent ground troops to invade Gaza.
The poll of 503 respondents had an error margin of 4.5 percentage points.
The same survey showed Prime Minister Benjamin Netanyahu's Likud Party and electoral partner Israel Beiteinu losing some support, but his hard-line bloc still able to form the next government. Elections are to be held on Jan 22.