The three were among a group of four people targeted as they approached the Egyptian border on Wednesday, Aljazeera's correspondent reported.
Israeli military sources confirmed troops shot at a group of men spotted near the frontier at Rafah.
"The figures appeared to be either terrorists en route to an attack or arms smugglers. Our forces opened fire, hitting at least one of them," a military source said.
Rafah sees frequent smuggling of arms from Egypt, prompting Israeli raids and clashes with resistance fighters.
It was not immediately clear if the dead men were civilians or belonged to resistance groups waging a four-year-old uprising in Gaza and the West Bank against Israeli occupation.
Palestinians said the Israeli military late on Wednesday handed over the bodies of the three Palestinians.
Mourners carry the body of Mumin
Rajab during his funeral in Gaza
Earlier, the bodies of two Hamas fighters killed in a gun battle with Israeli forces in the Gaza Strip were handed over to Palestinian authorities before being buried.
Mumin Rajab and Adham Ehgalala were both shot dead on Tuesday morning, following an ambush near the Karni border crossing between Israel and Gaza that killed an Israeli soldier.
Hamas had previously claimed that two of its fighters had taken part in an operation in the area.
Both men were aged 22 and from the nearby al-Shijaiya neighbourhood of Gaza City where two members of another Palestinian movement, Islamic Jihad, were killed on Tuesday by an unmanned Israeli spy plane.
The latest deaths brought the overall toll since the September 2000 start of the intifada to 4601 people killed, including 3564 Palestinians and 963 Israelis, according to an AFP count.