JERUSALEM — An Israeli man at work on a kibbutz and an 8-year-old Palestinian Arab girl at play in the Gaza Strip died yesterday in aerial combat between Israel and Hamas, a spike in cross-border violence that could set back Egypt’s effort to forge a truce.

A mortar fired at midday from near the Gaza town of Khan Yunis struck a paint factory on the Nir Oz kibbutz about 2 1/2 miles away, killing 51-year-old Amnon Rosenberg.

About two hours later, an Israeli jet launched a missile at Hamas militants close to the source of the mortar fire, the army said. The missile missed the target and killed Ayah Najar as she played outside her home, according to Palestinian Arab medical workers.

The Israeli-Gazan border had been relatively quiet in recent weeks as Egyptian mediators passed messages back and forth. But the peace effort had begun to stall, and yesterday’s bloodshed indicated that Israel and Hamas are running out of patience.

Hamas, an Islamic group that calls for Israel’s destruction, claimed responsibility for firing three mortar rounds and called the attack an answer to “nonstop aggression against our people.” The fatal 120-millimeter shell left four other workers wounded in the southern Israeli factory’s storage area.

An Israeli government spokesman, David Baker, said Hamas “will be held accountable.” Israeli defense officials are to discuss a response with Prime Minister Olmert on Sunday after his return from Washington.

The Israeli officials are skeptical of a Hamas proposal for a six-month truce and are expected to consider stepped-up military action in Gaza, an option that Defense Minister Ehud Barak says is likely.