The most violent conflagration in more than a year between Israel and Gaza militants extended into a second day on Saturday, with airstrikes that destroyed residential buildings and killed five more people, according to Palestinian health officials.

The Israeli military said it had hit two Gaza residences belonging to operatives of the militant group Islamic Jihad that it described as weapons stores. Military officials said that prior warnings were given, and that the buildings were evacuated before the strikes.

Islamic Jihad and other smaller Palestinian militant groups in Gaza fired rockets at Israeli towns near the territory and cities farther afield in central Israel, including Tel Aviv, sending Israeli beachgoers rushing for cover.

The renewed tensions highlighted the challenge of preventing flare-ups in Israel and the occupied territories when both the Israeli and Palestinian leaderships are divided and politically weak, international attention is elsewhere and there is little hope of ending the 15-year blockade of the Gaza Strip by Israel and Egypt.

“There is no end in sight for this cycle, and no actor seems to wish to construct any more stable alternative,” said Prof. Nathan J. Brown, an expert on the Middle East at George Washington University.

This round of fighting, which began on Friday with Israeli airstrikes, has mainly pitted Israel against Islamic Jihad, the second-largest militant group in Gaza. Hamas, the dominant militia in Gaza, has so far stayed away from direct involvement, raising hopes that the conflict would not escalate into a larger war.

Yet, no cease-fire appeared imminent, despite early mediation efforts by foreign diplomats and the United Nations.

The five Palestinians killed on Saturday brought the two-day death toll to 15, according to health officials in Gaza. One of those killed on Friday was a 5-year-old girl.

At least two Israeli soldiers and a civilian were wounded, according to Israeli officials and news reports. But the majority of Palestinian rockets either fell on open areas or were intercepted by Israel’s Iron Dome air defense system, according to the military.

The only power plant in Gaza halted operations because of a freeze on fuel deliveries from Israel, further reducing power across large parts of the territory. A senior Israeli military official, speaking to reporters on Saturday on the condition of anonymity to comply with army rules, said Israel was liaising with Egypt about how to deliver more fuel to Gaza while under rocket fire.

When Israel launched the airstrikes on Friday, it said it was acting preemptively to prevent an imminent attack from Islamic Jihad in Gaza. Earlier in the week, Israel had arrested a senior figure from the group in the West Bank, leading to threats of reprisals. Israel said its airstrikes aimed to stop Islamic Jihad from following through on those threats.

One airstrike on Friday killed a senior Islamic Jihad commander in Gaza and the group returned fire with rocket and mortar barrages that sent thousands of Israelis into bomb shelters overnight Friday.

Since an 11-day war in May last year, Israel has persuaded militias in Gaza to avoid violence by offering 14,000 work permits to Palestinian laborers in the territory — the highest number since Hamas seized control of the territory in 2007.

Roughly two million people live in Gaza and most receive no direct benefit from the new permits. But the permits nevertheless provide a crucial financial lifeline to thousands of families in the enclave, where nearly one in two residents are unemployed and only one in 10 have direct access to clean water, according to UNICEF.

Wary of losing that concession, particularly while it is still rebuilding military infrastructure damaged during the last war, Hamas has avoided a major escalation all year in Gaza while still encouraging unrest and violence in Israel and the West Bank.

But Islamic Jihad, which, unlike Hamas, does not govern Gaza, is less motivated by small economic concessions.

This is at least the sixth surge of violence in Gaza since Hamas seized control in 2007, prompting Israel and Egypt to begin their blockade. Israel is not prepared to end the blockade while Hamas is in power, and while Hamas does not recognize Israel and refuses to end its armed activities.

In the absence of a formal peace process to end the conflict, the repeated rounds of violence in Gaza, as well as intermittent bursts of back channel diplomacy, are considered alternative ways to renegotiate the terms of the Gaza blockade.

“Absent anything more lasting, both sides resort to violence not to defeat the other side — much less eliminate it — but just to adjust the terms, and also to play to home audiences,” said Mr. Brown, the Middle East expert.

The last two days of conflict in Gaza can be linked back to a spike in violence across Israel and the West Bank several months ago. Rising Palestinian attacks on civilians in Israel in April and May led to an increase in Israeli raids on the West Bank, particularly in areas where Israeli officials said the attackers and their abettors came from.

The Israeli campaign resulted in almost nightly arrests across the West Bank over the past several months, and culminated in the arrest this week of Bassem Saadi, a senior Islamic Jihad figure.

The new round of violence also served as a reminder of Iran’s role in the Israeli-Palestinian conflict. While Tehran’s nuclear program is seen by Israel as the biggest threat, Iran also exerts regional influence by providing financial and logistical help to militant proxies across the Middle East, like Hezbollah, in Lebanon, and Islamic Jihad and Hamas in Gaza.

Israel’s opening strikes in Gaza came during a visit by Islamic Jihad’s leader, Ziad al-Nakhala, to Tehran to meet the group’s Iranian patrons — a factor that may have contributed to the group’s refusal to walk back its recent threats.

“Due to their full dependency on the Iranians, they have to do what the Iranians are telling them to do,” said Kobi Michael, a national security expert at the Institute for National Security Studies at Tel Aviv University.

The crisis was also the first major test for Yair Lapid, Israel’s caretaker prime minister who took office last month after his predecessor’s government collapsed.

The military operation is a risky gambit for Mr. Lapid, a centrist often derided for lacking security experience by his main rival, Benjamin Netanyahu, Israel’s longest serving prime minister, who now leads the opposition.

Although it gives Mr. Lapid the chance to prove his security credentials to the Israeli electorate, it also leaves him open to accusations that he is endangering both Israeli and Palestinian lives.

In Gaza, mourners were already counting the costs from the two days of fighting.

Relatives of Alaa Qadoum, the 5-year-old girl killed in an airstrike on Friday, wrapped her body in a white shroud and Palestinian flags on Friday. A bright pink bow tied most of her hair back.

“Alaa was a fun little girl who did not hurt anyone,” her grandfather, Riad Qadoum, 56, said in an interview. “She was not firing rockets or fighting anyone,” Mr. Qadoum said.

The senior Israeli military official who briefed reporters on Saturday said he was aware of the reports of her death and said any civilian deaths would be investigated. But Israel has in the past blamed militants for civilian deaths, saying they often station their rocket launchers and bases close to civilian homes and infrastructure.

In a separate briefing for reporters at a military base near the Gaza border in late July, senior Israeli military officials, speaking on the condition of anonymity under army rules, presented maps showing the routes of what they said were parts of a militant tunnel network, including sections running beneath roads around a major university in Gaza.

The length and scope of the fighting will partly depend on Hamas’s involvement.

Ismail Haniyeh, the leader of the political bureau of Hamas, said on Friday that the group was “open to all directions.”

But on Saturday, an Israeli military spokesman, Ran Kochav, told Israeli public radio that the fighting would last for at least a week.

On Sunday, tensions in Jerusalem could compound the situation, as Jews mark Tisha B’Av, which commemorates the destruction of two ancient Jewish temples, on a site now sacred to both Jews and Muslims. Large numbers of Jewish worshipers are expected to visit that site, known as the Aqsa Mosque compound or the Temple Mount.

Such visits often prompt unrest that has historically led to more rocket fire from Gaza.

Raja Abdulrahim, Carol Sutherland and Fady Hanona contributed reporting.