The men's deaths on Saturday were the first in the area since the Israeli army designated it a "no-go" zone, enforced by air strikes and artillery fire to curb rocket attacks on Israel by Palestinian resistance fighters.
The violence came as Hamas, which is sworn to destroying Israel, released a statement saying that Israel would "pay the price for its crimes committed against our people in northern Gaza".
Israel has demanded that Mahmoud Abbas, the Palestinian president, disarm gunmen as a condition to renewing a "road map" peace plan. Abbas has vowed to impose law and order after a spate of recent kidnappings and a surge of internal Palestinian unrest.
"It is time to impose the authority of law and order," Abbas said in a New Year message broadcast on Palestinian television on Saturday. "These events ... harm our international credibility and strengthen Israel's pretext to undermine peace and stop withdrawals."
His ruling Fatah faction faces a strong challenge from Hamas in parliamentary elections due on 25 January, despite Israeli and US objections to the group's participation in the polls.
Israel says its military action against Palestinian factions is a substitute for what it says is Abbas's inability to act against them. The Palestinian leader has preferred to negotiate with the groups.
Israel fears that Hamas could win many seats in parliament at the elections, which could threaten future peace talks. Israel says it will never negotiate with such groups.
Support for Hamas has grown since Israel withdrew from occupied Gaza last year after 38 years of military rule, and since a rift developed within Fatah.
Hamas gained control of large West Bank cities and much of the Gaza Strip in municipal elections last year.