JERUSALEM -- Cross-border hostilities between Gaza and Israel continued Saturday, a day after a temporary cease-fire expired. But the simmering exchanges were on a lower scale than the fighting that has raged for most of the past month, as Egypt-brokered efforts continued for a new cease-fire and a resumption of talks on a more durable end to the conflict.

But members of Israel's Cabinet urged the government to take steps to crush Hamas.

Israeli Minister of Intelligence and Strategic Affairs Yuval Steinitz said that should diplomacy fail to end the violence, "we won't have any choice but to defend ourselves and win this battle."

He told Channel 10 television that "this means that we will have to seriously consider the possibility of taking full control of Gaza for a number of weeks, maybe a month or two" to strip the Hamas-controlled territory of its rockets and weapons-manufacturing capabilities.

Eight Palestinians were reported killed in Israeli airstrikes, and Palestinian militants fired more rockets into Israel, but no new Israeli casualties were reported.

Hamas, the Islamist group that controls Gaza, had refused to extend the 72-hour cease-fire that expired at 8 a.m. Friday and immediately fired rockets into Israel. The group was frustrated with what Palestinian officials said was a failure by both Egypt and Israel to address Hamas' demands for a full lifting of the blockade on Gaza and the construction of a seaport.

The Israeli government accused Hamas of having violated the cease-fire after two rockets or mortar rounds were launched against Israel before dawn Friday. An official Palestinian statement said the attacks had resumed "after Israel withdrew from the cease-fire negotiations in Cairo." The Israeli delegation, which has traveled to and from Cairo for days, left Egypt at 7 a.m. Friday.

Tourism Minister Uzi Landau told Channel 10 today that Israel must "go after Hamas and defeat it" so other enemies of Israel aren't emboldened by the group's continued attacks. Landau also said that there can be no seaport in Gaza: "We can't open them the gate to a port so they can smuggle in heavy arms."

And while contacts between the Israelis and the Egyptians continued from afar, an official said Israel's delegation would not return to Cairo until a new cease-fire was in place.

Mushir al-Masri, a Hamas official in Gaza, said in an interview Saturday that the responses the Palestinian delegation in Cairo had received so far did not "meet the minimum level of the Palestinian people's aspirations, and there was no real response or acceptance of any of the main demands."

Al-Masri said the concessions Israel had offered so far were "partial" and "limited," and he accused the Israelis of wasting time "through political maneuvers."

Three Palestinians were killed early Saturday when an Israeli missile destroyed the Qassam Mosque in the Nusseirat refugee camp in the central Gaza Strip, and two cousins were killed in a separate strike as they rode a motorcycle east of Nusseirat, according to the Gaza Health Ministry and witnesses.

The mosque sits in a residential area of closely packed houses and alleys. A neighbor, Alaa Eid, a professor of journalism at Gaza's Al-Aqsa University, said Israel had called a man whose home is adjacent to the mosque and asked him to evacuate because the mosque was going to be hit.

Hearing the commotion, Eid woke his family, and they all left the house.

"Women, children and old men were all running, and they filled the alley," Eid said, describing the moments around 3:30 a.m. when an Israeli aircraft dropped a guiding or warning missile and then hit the mosque. He said it was unclear why the three people who were killed had been in the mosque at the time. About four hours after the strike, he said, a bulldozer and rescue teams came and dug their bodies out of the rubble.

The cousins killed on their motorcycle were identified by relatives as Abdel Hakim al-Mossadar, 60, and Hani al-Mossadar, 18. A spokesman for the Israeli military, speaking on the condition of anonymity under army rules, said they were "terror operatives." Relatives of the two said they had nothing to do with the resistance and were on their way to work at a family-owned gas station when they were hit.

Three more Palestinians were killed in airstrikes Saturday evening in Deir al-Balah and the southern city of Rafah. Two of them appeared to have been targeted as they rode in a car.

The Israeli military said it had struck more than 60 targets in the Gaza Strip since midnight, describing them as "terror activity sites, command and control centers, and weapon storage facilities."

It added that at least 28 rockets and mortars had been launched from Gaza by Saturday evening, of which 23 fell on open ground and five fell short, landing in Gaza.

More than 1,900 Palestinians, including hundreds of civilians, have died in the fighting, as have 64 soldiers and three civilians in Israel.

Meanwhile, people around the world have organized protests of Israel's actions in Gaza.

In central London, tens of thousands of people turned out in protest of the bombing of Gaza.

Large crowds of protesters marched through the British capital's busy West End shopping area on Saturday, passing the U.S. Embassy before descending on Hyde Park.

Many waved placards and the Palestinian flag, chanting "Free, Free Palestine!"

In New York, about 500 demonstrators walked to the United Nations on Manhattan's East Side after gathering behind police barricades off Columbus Circle to protest Israeli actions in the Gaza Strip.

Information for this article was contributed by Isabel Kershner and Fares Akram of The New York Times; by Gwen Ackerman and Saud Abu Ramadan of Bloomberg News and by Verena Dobnik and staff members of The Associated Press.

A Section on 08/10/2014