At least twelve others were wounded in the missile strike that targeted buildings and a car as it was leaving the base.
Palestinian security and medical sources have said that an Israeli aircraft fired three missiles at a training base of the militant popular Resistance Committees (PRC) group in the town of Rafah.
A doctor at the town's hospital, Ali Moussa, confirmed that six people were killed in the raid including a local PRC leader, Iyad Abu al-Aynin, and his 7-year-old child.
Abu al-Aynin, a bomb maker, had brought his daughter and son to watch training exercises at the base. The son was wounded.
The Israeli army claimed a car carrying several "terrorists" was hit as it left the base near the town of Rafah on the border with Egypt.
"The vehicle was coming out of a training camp in which both training and weapons training were being conducted," an Israeli army spokesman said.
Warnings of reprisals
The armed wing of Hamas warned of quick retaliation after the deadliest Israeli strike in five months.
"The Palestinian resistance with all its factions will not stand handcuffed against these crimes and the enemy will pay.
“The coming days will prove the truthfulness of our promises and the enemy should watch and wait," the armed wing said in a statement.
The Islamic militant group took over the Palestinian government last week after a resounding win in parliamentary elections in January.
Hamas's armed wing has largely abided by a year-old truce and facing increasing international pressure to moderate has toned down its rhetoric in recent months.
Call for international action
A spokesman for Palestinian President Mahmoud Abbas, Nabil Abu Rdainah, condemned the air strikes and urged the international community to intervene in what he called a serious escalation by Israel.
"We demand the Israeli government immediately stop the aggression," Mr Rdainah told reporters in Gaza.
It comes as Mr Abbas was holding a late-night meeting with Ismail Haniyeh, the new prime minister of the Hamas-led government.
But Israel insists it has the right to strike at militants it says are planning attacks on the Jewish state.
In recent days the Israeli military stepped up air strikes and artillery barrages into Gaza in response to regular rocket fire from the area. Israel withdrew from Gaza last year after 38 years of occupation.
Aid frozen
Also on Friday Mr Haniya and Mr Abbas denounced the European Union and the United States for suspending aid payments, warning the move punished ordinary people for the democratic choice.
"These decisions were hasty and unjust," Mr Haniya said in a press conference following his meeting with Mr Abbas.
"The world should respect the choice of the Palestinian people," the senior member of the Islamic radical Hamas movement said.
By cutting the aid, the United States and EU were "punishing all the people, workers and families," Mr Abbas said.
The European Commission, the executive arm of the EU, it warned that it could not provide aid to a Hamas-led government unless the militant group renounces violence and recognises Israel.