The health official said the Palestinians killed in the Israeli attack included six gunmen and three civilians and that at least 12 of the wounded had been taken to hospital.
An Israeli army spokesman said the military operation began after several groups of Palestinian gunmen were detected near the border and one of the groups fired a rocket towards Israel.
One of those killed by Israeli forces was believed to be the son of senior Hamas leader Mahmoud al-Zahar.
A foreign worker, a 20-year-old from Quito, Ecuador, was also shot dead by a Palestinian sniper as he was working in a field on an Israeli farm close to the border with Gaza.
According to Israel, there are some 20,000 militants 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 insurgents.
The Gaza Strip was seized by hard-line Islamic group Hamas last June from Palestinian President Mahmoud Abbas' Fatah movement.
Israeli Prime Minister Ehud Olmert spoke on Monday against an invasion of the Gaza Strip, despite continuing rocket attacks by Palestinian militants from the enclave.
Olmert called the current Gaza Strip conflict a war that Israel was waging wisely, restricting its actions to pinpoint air bombings and localized ground raids in border regions.
He said he "very much recommends that we not get ourselves embroiled in operations and in [paying] prices that are disproportionate to the constraints we are dealing with."
