Infantry units backed by tanks stormed into Beit Hanoun town overnight, surrounding and blocking access to the hospital and establishing control over the town, medical officials and witnesses said on Wednesday.
Al Jazeera's Palestinian correspondent said the Israeli military has announced the death of an Israeli soldier during the Bait Hanun operation.
Hamas' armed wing said it had killed the Israeli soldier and wounded several others.
Witnesses said that five Palestinian gunmen were killed by the Israeli military including four from Hamas.
The action was aimed at stopping rocket fire, an Israeli military spokesman said, adding that Palestinian fighters had fired 300 rockets from Beit Hanoun into Israel since the start of the year.
Ismail Haniya, the Palestinian prime minister, denounced the the attacks as a "massacre".
Israeli soldiers preparing for
the raid into northern Gaza
He said he hoped the violence would not derail Egyptian-brokered talks trying to arrange a swap of Palestinian prisoners in Israel for the release of the captive soldier.
Mahmoud Abbas, the Palestinian president, said Israel was waging "all-out war", and called the operation "despicable".
The latest incursion came days after Ehud Olmert, the Israeli prime minister, said that Israel could expand its four-month offensive in the coastal strip, which has already left more than 260 Palestinians and two Israeli soldiers dead.
Olmert was quoted as telling MPs in Jerusalem on Monday that the army was "preparing for an even more extensive operation in the Gaza Strip".
Later, six homemade rockets were fired at the Israeli border town of Sderot from northern Gaza. Israeli medical officials said two rockets hit the town, lightly wounding one person.
In another development, Amir Peretz, Israel's defence minister, has said a Saudi peace initiative can be a "basis for negotiation", indicating a new possibility to resume talks with the Palestinians after years of stalemate.
"We could see the Saudi initiative as the basis for negotiation. This does not mean that we are adopting the Saudi initiative, but it can serve as a basis," Peretz told an academic conference at Tel Aviv University on Tuesday night.
Bodies of Palestinians killed in
an Israeli raid on Bait Lahiya
The Saudi plan, first proposed in 2002, calls for a comprehensive peace between Israel and the Arab world, based on a complete Israeli withdrawal from lands it captured in the 1967 Middle East war - the West Bank, Gaza Strip, East Jerusalem and Golan Heights.
Peretz is the most senior Israeli official to publicly consider it.