The death took place during clashes between Israeli soldiers and Palestinian fighters on Tuesday near the Kissufim crossing with Israel, east of Khan Yunus, in the Gaza Strip.
Witnesses said the fighters had exchanged fire with Israeli soldiers in an area of central Gaza after troops backed by tanks had moved across the border just after dawn.
The soldier died after sustaining serious injuries, Aljazeera said.
Afterwards, Aljazeera's correspondent said the channel's Gaza bureau received a joint statement issued by Hamas's Izz al-Din al-Qassam Brigades and the National Resistance Committees, claiming responsibility for the killing of "an Israeli officer participating in the incursion in southern al-Maghazi and northern Kissufim, south of Gaza Strip".
Two Palestinian fighters belonging to the two factions, ambushed Israeli soldiers in a spot 500 metres away from the border separating Gaza Strip from Israeli territories, the statement said.
Clashes then erupted with Israeli forces, resulting in the death of the officer and injuries to others, the statement added.
Aljazeera's correspondent added that the Israeli army had yet to identify the slain soldier.
The Israeli army confirmed that one of its soldiers was killed during an operation in the Gaza Strip on Tuesday.
"An Israeli soldier was killed during an anti-terrorist operation ... in the centre of the Gaza Strip," an army spokesman told AFP.
Earlier, an Israeli air strike destroyed the two-storey central Gaza home of a senior security official in the interior ministry, witnesses said. No one was wounded in the operation.
An Israeli army spokesman said the house was hit because it was being used to store weapons.
In addition to serving in the interior ministry, the official is a member of Hamas, Palestinian officials said.
Tuesday's clash came one day after Palestinian factions agreed to form a unity government to try to end Western sanctions imposed on the Hamas-led administration for refusing to recognise Israel and renounce violence.
Israel has responded sceptically to the unity government while the Hamas Islamist movement has said it would never recognise Israel.
Israel has frequently hit Palestinian fighters' homes as part of a broader Gaza offensive launched after an Israeli soldier was seized and two others killed in a cross-border raid on June 25.
The Israeli offensive has killed more than 210 Palestinians, about half of them civilians.