In one incident captured by Associated Press video, several dozen Palestinians, most young men, approached the fence, coming close to a group of Israeli soldiers on the other side.
Some Palestinians briefly talked to the soldiers, while others appeared to be taunting them with chants of "God is Great" and "Morsi, Morsi," in praise of Egyptian President Mohammed Morsi, whose mediation led to the truce.
At one point, a soldier shouted in Hebrew, "Go there before I shoot you," and pointed away from the fence, toward Gaza. The soldier then dropped to one knee, assuming a firing position. Eventually, a burst of automatic fire was heard, but it was not clear whether any of the casualties were from this incident.
Gaza health official Ashraf al-Kidra said a 20-year-old man was killed and 19 people were wounded by Israeli fire near the border.
During the incidents, Hamas security tried to defuse the situation and keep the crowds away from the fence.
Moussa Abu Marzouk, a top Hamas official at the ongoing negotiations in Cairo, told the AP that the violence would have no effect on the cease-fire.
The crowds also included farmers hoping to once again farm lands in the buffer zone. Speaking by phone from the buffer zone, 19-year-old Ali Abu Taimah said he and his father were checking three acres of family land that have been fallow for several years. "When we go to our land, we are telling the occupation [Israel] that we are not afraid at all," he said.
Israel's military said roughly 300 Palestinians approached the security fence at different points, tried to damage it and cross into Israel. Soldiers fired warning shots in the air, and after the Palestinians refused to move back, troops fired at their legs, the military said.
The truce allowed both Hamas and Israeli Prime Minister Benjamin Netanyahu to step back from the brink of a full-fledged war. Over eight days, Israel's aircraft carried out about 1,500 strikes on Hamas-linked targets, while Gaza fighters fired roughly the same number of rockets at Israel.
A poll Friday showed about half of Israelis thinks their government should have continued its Gaza offensive. The independent Maagar Mohot poll showed 49 percent of respondents felt Israel should have kept pursuing squads that fire rockets into Israel, 31 percent supported the decision to stop, and 20 percent had no opinion.