A health official in the Gaza Strip said 45 Palestinians were wounded in the fighting, involving Israeli tanks and helicopters. The official said most of those killed were gunmen, but several were civilians. At least 12 of the injured are reportedly in a critical condition.
An Israeli army spokesman said the operation began after several groups of Palestinian gunmen were spotted near the border, and one of the groups fired a rocket towards Israel.
One of those killed by Israeli forces was Hussam Zahar, the 24-year-old son of senior Hamas leader Mahmoud al-Zahar.
A 20-year-old from Quito, Ecuador, was also shot dead while working on a field at an Israeli farm close to the border with Gaza.
According to Israel, there are around 20,000 militants active in the Gaza Strip, many receiving regular financial and logistical support from abroad. In the last two years, Israeli military and secret services have killed about 1,000 Palestinian fighters.
The Gaza Strip was seized by hard-line Islamic group Hamas last June from Palestinian President Mahmoud Abbas' Fatah movement. The latest Israeli operation has seen one of the largest death tolls since Hamas took over the enclave.
Israeli Prime Minister Ehud Olmert spoke on Monday against a large-scale cross-border incursion into the Gaza Strip, despite continuing rocket attacks by Palestinian militants.
Olmert called the current conflict a war that Israel was waging prudently, restricting its actions to pinpoint air bombings and localized ground raids in border regions.
He said he "very much recommends that we do not get ourselves embroiled in operations and in [paying] prices that are disproportionate to the constraints we are dealing with."
