Thursday's pause in the 13-day Israeli offensive to allow humanitarian aid into the strip was scheduled to last from 1pm (11:00 GMT) to 4pm (14:00 GMT).
The Israeli military said that it was checking reports of the incident.
John Ging, the head of the UN relief agency in Gaza, said that the casualties were Palestinian civilian contractors contracted to bring supplies from the crossing points.
"They were co-ordinating their movements with the Israelis, as they always do, only to find themselves being fired at from the ground troops," he told Al Jazeera.
"It has resulted tragically in the death of one and the injury of two others."
Wednesday's three-hour ceasefire allowed beleaguered Gazans and aid workers to recover dead bodies, treat the wounded, and gather much-needed supplies in and around Gaza City.
Rafah bombarded
Earlier on Thursday, thousands of Palestinians fled their homes in the southern Gaza Strip as Israeli forces bombarded Rafah after dropping leaflets to warn local residents about an impending blitz.
Witnesses said that homes, suspected smuggling tunnels and a mosque were hit in the area along the Egyptian border early on Thursday.
The leaflets warned that that the Israeli military "will bomb the area due to its use by terrorists to [dig] tunnels and to stock up" on weapons.
Hundreds of tunnels are believed to cross under the Egyptian border around Rafah allowing Palestinians to smuggle in basic supplies, in short supply due to the Israeli blockade, and weapons.
An Israeli army spokeswoman said the military dropped the flyers "as in the past to avoid civilian casualties".
At least 700 Palestinians, including 219 children, have died in Gaza since Israel began its assault on December 27. More than 3,080 people have also been wounded.
Eight Israeli soldiers and three civilians have died in the same period.
Besieged Gazans
Al Jazeera's Ayman Mohyeldin, reporting from Gaza City, said the flyers would have frightened the civilian population of southern Gaza.
"Israel has cut the northern part of Gaza from the southern part. Those in the southern part wouldn't be able to go to the north seeking refuge and vice versa," he said.
Mohyeldin said there was also another night of heavy bombardment in the north around Gaza City.
"Most of the targets hit throughout the northern part of the territory included mosques and homes that have been previously struck on the previous days of this conflict. Some of the government buildings and police stations that were nearly destroyed are now completely levelled," he said.
The AFP news agency quoted witnesses as saying that dozens of Israeli tanks had entered southern Gaza and were heading towards Rafah.
Fierce fighting was also reported between Palestinian fighters and Israeli soldiers around Khan Yunis.
It was unclear if the latest offensive was the "third stage" of the offensive approved by the Israeli security cabinet on Wednesday.
A senior Israeli defence official said a meeting chaired by Ehud Olmert, the prime minister, had "approved continuing the ground offensive, including a third stage that would broaden it by pushing deeper into populated areas".
'Shocking' incident
The International Committee for the Red Cross (ICRC) on Thursday accused the Israeli military of not helping wounded Palestinians in an incident in Gaza City that it described as "shocking".
ICRC and Palestinian Red Crescent workers said in a statement that several wounded Palestinians and four weakened children were found alongside 12 dead bodies in houses hit by shelling in Zaytun, less than 100 metres from Israeli positions.
"The ICRC believes that in this instance the Israeli military failed to meet its obligation under international humanitarian law to care for and evacuate the wounded," it said.
The Red Cross team, including four ambulances, had only gained safe passage from Israeli army to access the neighbourhood on January 7 after trying for four days, the ICRC said.
Meanwhile, Israeli security forces in the occupied West Bank shot dead a Palestinian in a confrontation at a Jewish settlement near Jerusalem, Israeli radio reported.
