The truce, which calls for an end to Gaza rocket fire on Israel and Israeli airstrikes on Gaza, came after eight days of cross-border fighting, the bloodiest between Israel and Hamas in four years.
In a letter to the U.N. Security Council, the Palestinian U.N. observer Riyad Mansour called the situation in Gaza "extremely fragile" and said Israel's cease-fire violations and other illegal actions risk undermining the calm that was just restored.
Hundreds of Palestinians approached the border fence Friday in several locations in southern Gaza, testing expectations Israel would no longer enforce a 300-meter-wide (300-yard-wide) no-go zone on the Palestinian side of the fence that was meant to prevent infiltrations into Israel. In the past, Israeli soldiers routinely opened fire on those who crossed into the zone.
In one incident captured by Associated Press video, several dozen Palestinians, most of them young men, approached the fence, coming close to a group of Israeli soldiers standing 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.
Mansour, the Palestinian U.N. observer, said Israeli forces fatally shot Anwar Abdulhadi Qudaih, 21, in the head and injured at least 19 other Palestinian civilians in a border area east of Khan Younis.
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 Associated Press that the violence would have no effect on the ceasefire.
The crowds were mainly made up of young men but 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, but after the Palestinians refused to move back, troops fired at their legs, the military said. A Palestinian infiltrated into Israel during the unrest, but was returned to Gaza, it 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 some 1,500 strikes on Hamas-linked targets, while Gaza fighters fired roughly the same number of rockets at Israel.
The fighting killed 166 Palestinians, including scores of civilians, and six Israelis. Mansour, the Palestinian U.N. envoy, said more than 1,230 Palestinians were injured, predominantly women and children.
In Cairo, Egypt is hosting separate talks with Israeli and Hamas envoys on the next phase of the cease-fire - a new border deal for blockaded Gaza. Hamas demands an end to border restrictions, while Israel insists Hamas halt weapons smuggling to Gaza.
Mansour also accused Israel of intensifying its use of "excessive and lethal force" against Palestinian civilians in the West Bank and East Jerusalem in recent days and of arresting at least 230 Palestinian civilians since the Gaza fighting began, including several members of the Palestinian Legislative Council who were detained at dawn Friday.
The Palestinian U.N. observer called on the Security Council and the international community "to remain vigilant in their demands for a complete cessation of hostilities and for compliance by 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. Twenty-nine percent thought Israel should have sent ground troops into Gaza. The poll of 503 respondents had an error margin of 4.5 percentage points.
The same survey showed Netanyahu's Likud Party and electoral partner Israel Beiteinu losing some support, but his hard-line bloc was still favored to form the next government after Jan. 22 elections.___
Associated Press writers Ibrahim Barzak in Gaza City and Amy Teibel in Jerusalem contributed reporting.