Medical sources and witnesses said Egyptian border guards opened fire on Nafez Attiyeh, 34, while he approached a security fence at the border.
Medics said he was shot in the head. A second Palestinian was wounded when he was shot in the thigh.
But Aljazeera's correspondent in Cairo quoted Egyptian presidential spokesman Suleiman Awad as denying that Egyptian border guards had opened fire at Palestinians.
The reported shootings come amid chaotic scenes at the border where dozens of Palestinians, including armed resistance fighters, swarmed into part of the buffer zone abandoned by Israeli troops who left Gaza early on Monday.
Barricades knocked down
In one section in the divided border town of Rafah, dozens of joyous youngsters entered the no-man's land on the Egyptian side after toppling a barbed wire barricade on a concrete wall that marks the frontier.
Some Egyptian security officials said they had allowed some crossings to take place as a "humanitarian" gesture to let people separated for years reunite.
Many Palestinians have entered
into previously banned Gaza areas
But they indicated that free, unchecked crossings would be short-lived as Egypt deploys 750 heavily armed troops to secure its border with Gaza following the end of Israel's 38-year occupation.
First few crossings
Two walls - one Egyptian and the other long guarded by
Israel - run through Rafah separated by a narrow strip.
Egyptian security forces stood by as hundreds of Egyptians and Palestinians helped people climb over the fences at will and join the spontaneous celebrations held under a scorching sun.
"Before, no one could get near this area. They would be either shot or captured," said one of the Egyptian policeman who are being replaced by the incoming border guards.
"It is only for today, but you can see there is chaos," a policeman added.
But even if it is just for a day, some were pleased to cross the lines.
One woman, 22-year-old Maisaa Fayez, screamed out: "Aunty! Are you my aunt? Do you know who I am?" as she leaned to the Palestinian side to embrace a woman who broke into tears.
And 18-year-old Muhammad Salem, who climbed over the two walls from Palestinian Rafa said: "My mum wanted to come as well but she wasn't able to climb the ropes … This is not just the beginning, this is victory. All the people are happy."
Goods such as fish, chocolate and cigarettes also crossed the fences easily, with Egyptian police stepping in occasionally to confiscate some of the contraband.