JERUSALEM — Cross-border fighting between Israel and Palestinian militant groups in Gaza continued for a fourth day on Monday, with the Palestinian death toll rising from Israeli airstrikes and the militants’ rockets reaching farther into Israel.

Yet there was no sign that either Israel or Hamas, the Islamic militant group that rules Gaza, wanted an all-out confrontation. The prospects of an imminent showdown, like the one that led to Israel’s three-week offensive in the winter of 2008-9, seemed unlikely. Some of the old rules of the conflict have changed since then, and new domestic and regional factors have emerged.

For Israel, the success of its recently deployed Iron Dome antirocket missile system has had an impact. Since the hostilities began on Friday, the missile batteries have managed to intercept 54 of the nearly 70 Palestinian rockets that were aimed at the major cities of the south, the Israeli military said.

The prevention of mass casualties and damage has reduced pressure on the country’s leaders to embark on a major military operation in Gaza and given them more time to weigh their options, according to Israeli officials and experts.

“There is a serious strategic change here,” Dan Meridor, the minister of intelligence and atomic energy, told Israel Radio on Monday. “Years ago, it was not simple to incorporate into Israeli military doctrine the great importance of defense.”

The regional changes of the past year are also playing a role in the calculations of both Israel and the Islamic groups.

Since the overthrow of President Hosni Mubarak of Egypt, a close ally of Israel, and the rise of Islamic political parties there, Israel has been aware that there is less tolerance in Cairo for a major Israeli offensive in Gaza. The Israel-Egypt peace treaty is already under strain.

“The interim situation in Egypt is unclear,” Ehud Yaari, an Israel-based fellow of the Washington Institute for Near East Policy, said in an interview. “Israel has no interest in putting the Egyptians to the test.”

Hamas has been involved in a delicate balancing act, allowing the smaller militant groups like Islamic Jihad to avenge the deaths of their comrades in Israeli airstrikes but at the same time urging a restoration of calm.

Islamic Jihad, the group firing most of the rockets in this round of violence, is challenging Hamas in Gaza. The chief of Islamic Jihad, which is backed by Iran, has remained in Syria. The Hamas leadership recently abandoned its base there and expressed its support for the Syrian people in their struggle against President Bashar al-Assad.

Mkhaimar Abusada, a political science professor at Al-Azhar University in Gaza, said that Hamas, as the ruling power in Gaza, feels it has more responsibility than other groups and knows that any confrontation with Israel would cost it dearly. Islamic Jihad, he added, wants to demonstrate that it is not switching sides and abandoning Syria.

Israel’s military chief of staff, Lt. Gen. Benny Gantz, has warned in recent months that the repeated rounds of violence in the south will eventually require Israel to carry out another large-scale military operation in Gaza.

The finance minister, Yuval Steinitz, also told reporters on Sunday that “Israel cannot accept in the long run a Hamas and Islamic Jihad regime in Gaza, and sooner or later, and I don’t want to quote dates, we will have to do a ‘root canal.’ ”

But the prevailing sense in Israel is that now is not the time. Some Israeli politicians have warned that a major conflagration would divert world attention from what Israel considers the more existential threat of a nuclear Iran.

Israeli officials confirmed that Hamas had sent messages via Egypt asking to restore the informal cease-fire that had largely been in effect since the last round of fighting.

Israel said it would continue to act in Gaza as long as necessary. A spokesman for Islamic Jihad implicitly criticized Hamas for running from conflict after a lull, telling reporters in Gaza on Monday that from now on, “the resistance would impose conditions for any truce.”

In the meantime, there remained a risk that hostilities could escalate.

More than 150 rockets have fallen in Israeli territory since Friday, and Gaza officials said at least six Palestinians died on Monday, bringing the overall toll to 24. Though most of those killed have been militants, at least two of those who died in airstrikes on Monday were civilians.

A Gaza medical official and Gaza human rights groups said that one of the victims, Nayif Shaaban Qarmout, 14, was killed in an airstrike and that five other youths were wounded as they walked to school, but the Israeli military denied having carried out any attacks at that hour. An Agence France-Presse reporter at the scene confirmed that there was no sign of an airstrike.

Later, a missile killed Muhammad al-Hassumi, 65, and his daughter Fayza, 30, as they put out a fire on their land. The Mezan Center for Human Rights in Gaza said the fire had been caused by a Palestinian rocket that fell short of its target.

The Israeli military said it had aimed at a squad preparing to launch rockets from within a residential area of northern Gaza. It blamed the Palestinian groups for operating from urban areas and using civilians as “human shields.”

Two of the Palestinians’ rockets struck near Gedera, Israel, about 17 miles southeast of Tel Aviv. Another slammed into the center of Ashdod, a major Israeli port city, causing widespread panic, shattering storefronts and damaging buildings and cars.

The United Nations secretary general, Ban Ki-moon, said he was “gravely concerned at the latest escalation between Gaza and Israel, and once again civilians are paying a terrible price.” Mr. Ban told the Security Council that rocket attacks on Israeli civilians were “unacceptable,” but he urged Israel to “exercise maximum restraint.”