The incursion precipitated the heaviest fighting since Israeli forces converged on Gaza eight days ago in response to the abduction of the 19-year-old army corporal Gilad Shalit and the firing of Qassam rockets.
In the northern Gaza Strip, six people were killed and dozens wounded in what the army said had been three separate aerial strikes aimed at gunmen.
Elsewhere, Palestinian sources said that eight people, including civilians, were among victims of separate attacks, at least one of whom had been killed by an unmanned aerial drone. Five Palestinian militants were later killed in two missile strikes on cars.
The Israeli soldier died after being shot by a Palestinian sniper in a Beit Lahiya house taken over by his unit. Said Siyam, the Palestinian Interior Minister and Hamas leader, last night called on security service personnel fulfill their "duty to stand up to this aggression and cowardly Zionist invasion".
Amir Peretz, Israel's Defence Minister, insisted yesterday: "We have no intention of drowning in the Gaza swamp." He said later: "Return Gilad alive and healthy, stop firing rockets and we will return our soldiers to their bases."
Arab states yesterday called on the UN Security Council to demand that Israeli forces immediately withdraw from Gaza, but France and the US criticised their proposed resolution as unbalanced.
With little sign of a breakthrough in the continuing international diplomatic efforts to broker a solution to the crisis, the fighting between a heavily armoured Israeli incursion force with air support and militants in the northern Strip was the most serious since the disengagement from Gaza ordered by Ariel Sharon last August.
Two other Hamas gunmen, among many who converged on the area with anti-tank and other missiles, were killed in an earlier incident in northern Gaza. And two Palestinians were killed in a separate Israeli air strike outside the southern Gaza town of Khan Yunis. The Israeli military said that both had been militants seeking to attack its forces while Palestinian sources said that one had been a civilian.
But the heaviest machine gun fire and most casualties were in western Beit Lahiya as Israeli forces, with tanks, armoured vehicles, drones and helicopter gunships, sought to secure control of the north-west corner of the Gaza Strip, a sector bounded by five kilometres of the northern border and about the same length of the Mediterranean coast. The area includes the ruins of the three northernmost former Jewish settlements abandoned last August and the Atatra district of Beit Lahiya.
Although most of the dead were militants, one civilian who was killed was Mohammed al-Atta, 25. His uncle, Abdul Ahmed al-Atta, 34, a taxi driver, said he had been at home with his nephew, wife and children when a tank fired at the house. Mr Atta, his shirt caked with blood from carrying his nephew to the ambulance, said: "They targeted our house; there was shooting and then I saw my nephew on the ground. There was a tank 100 metres away. We are civilians and there was no resistance in the area at the time."
He added that the Israeli forces had entered the area at about 7am, advancing through orchards rather than using the main streets.
Mr Atta said there had been a long delay after he called an ambulance, which he understood was because Palestinian liaison officers had been unable to co-ordinate safe passage with the Israeli military for emergency vehicles through the area and said he was obliged to telephone a friend in the Red Cross before the co-ordination could take place.
His nephew died on the way to hospital. The army said it had not been able to verify the incident. A group of relatives and friends stormed the ambulancemen's quarters shouting that they had received calls telling them that ambulances had still not arrived to pick up two other dead neighbours and several wounded.
There was no immediate confirmation of the civilian deaths in Atatra. Ambulances were forced to wait near the American School in Atatra for clearance as heavy machine-gun fire from Israeli armoured vehicles, as well as semi-automatic gunfire from militants, sounded across the district.
Later, mourners for the militants who marched through Gaza City were told through a loudspeaker that there would be a "response from Hamas to what Israel is doing."
With Israel still rejecting any suggestion of a prisoner exchange to secure the release of Cpl Shalit, the captured soldier's father Noam said: "In the end, it will be necessary to pay a price for Gilad's freedom. I don't understand why the government is delaying negotiations on this price."