The renewed exchanges have dashed hopes for a lasting truce after a monthlong war that has already killed over 2,000 people.
By midmorning Friday, Israel had launched about 20 airstrikes at Gaza, while Gaza militants fired two rockets at Israel, the Israeli military said.
Earlier this week, Hamas rejected an Egyptian truce proposal under which Israel would gradually ease its blockade of Gaza, without giving specific commitments.
Hamas demands a lifting of the border closure, imposed by Israel and Egypt after the militant group's takeover of the coastal strip in 2007.
More From This Section
Responding to the killing of the three, senior Hamas political leader Ismail Haniyeh said yesterday that his group would not budge from its demands.
"We will not accept anything less than an end to the (Israeli) aggression and an end to the blockade," Haniyeh said in a statement posted by the Hamas-affiliated Al Rai news service.
"Anyone involved in cease-fire efforts must understand that our people will not accept anything less than this."
Nearly a quarter of the dead, 469, are children, according to the top UNICEF field officer in Gaza, Pernilla Ironside.
Of the more than 10,400 Palestinians wounded, nearly a third are children, according to UNICEF figures, while some 100,000 Gazans have been left homeless.