Three Israeli soldiers have been killed in fighting in the northern Gaza Strip, the military said on Tuesday.

The soldiers' deaths were announced hours after Hamas' armed wing said on Monday its fighters were engaging in "fierce clashes" with Israeli forces in the north of the territory.

Israel began its offensive in Gaza after Hamas militants burst through the border from Israeli-blockaded Gaza, attacking Israelis in homes, cars and at an all-night music festival. Israel says 1,200 people were killed and 251 people taken as hostages into Gaza. An additional four were already held by Hamas.

Israel's campaign has devastated much of Gaza, killing more than 54,000 Palestinians and destroying most buildings. Much of the population now lives in shelters in makeshift camps.