Hamas rejected Secretary of State John F. Kerry’s call for a cease-fire amid concerns that an agreement won’t be reached before other parties are drawn into its conflict with Israel.

A new jihadi media outlet called Al Fawaris released a video Wednesday calling on Gazans to endure the military operation. Its message said victory looms and that Muslims all over the world support them.

While Hamas is using tactics favored by Hezbollah, the Lebanon-based Islamist group has not shown signs of entering the conflict. Analysts say Hezbollah, which has offered words of support for Hamas, is fully occupied with Syria’s civil war.

“Right now, Hezbollah has way too much invested in the Syrian conflict to provoke an unnecessarily destructive war with Israel,” said Daniel Nisman, president of the Levantine Group, a geopolitical risk and research group based in Tel Aviv.

The Middle East Media Research Institute’s Jihad and Terrorism Threat Monitor published a report with a video featuring jihadi cleric Abu hareth Al-Maqdisi, who said he and his fighters in Syria want to join the battle in Gaza.

“True, we are fighting in Syria, but our heart yearns to arrive and fight the sons and brothers of the apes and pigs [the Jews],” the institute reported Al-Maqdisi as saying. The jihadi cleric said Gazans must be patient and wait for either victory or martyrdom, and that Allah will soon send “extraordinary soldiers who will fight and defeat the Jews.”

Mr. Kerry reported progress in indirect negotiations, and Hamas leader Khaled Meshaal called for a temporary truce to allow humanitarian relief into Gaza. But Mr. Meshaal said his group would keep fighting Israel and would not agree to a more lasting cease-fire without a full negotiation of terms.

“We need the calm for a few hours to evacuate the wounded and assist in the relief. This means a real truce backed by a real relief program offered to the people of Gaza,” Mr. Meshaal said at a news conference in Qatar.

However, he said any permanent cease-fire could be reached only if Israel ends its siege and could be implemented only after full negotiations.

More than 680 Palestinians and 34 Israelis have been killed since fighting began in early July.

Already hurt by mass tourism cancellations, Israel faced increased economic pressure after the U.S. Federal Aviation Administration took the rare step Tuesday of banning flights to Tel Aviv and renewed the order Wednesday. Many other foreign carriers, on heightened alert after a Malaysian airliner was shot down over a combat zone in Ukraine last week, followed suit. Israeli carriers continued to operate.

“Hamas‘ success in closing the Israeli airspace is a great victory for the resistance, a terrible failure for Israel that wrecks the image of Israeli deterrence,” said Hamas spokesman Sami Abu Zuhri. The Tel Aviv stock exchange and shekel were flat, with traders showing little concern about the flight stoppages.

Mr. Kerry landed at Ben Gurion International Airport in Tel Aviv on Wednesday, despite the flight bans, and met with Palestinian President Mahmoud Abbas, U.N. Secretary-General Ban Ki-moon and a grim-faced Israeli Prime Minister Benjamin Netanyahu. He said indirect talks had made some progress but returned later to Egypt, which shares a border with Gaza and has mediated with Hamas.

“We have certainly made some steps forward. There is still work to be done,” said Mr. Kerry, whose most recent efforts at peace negotiations between Mr. Netanyahu and Mr. Abbas broke down in April.

Mr. Kerry has been working through Mr. Abbas, Egypt and other regional proxies because the U.S., like Israel, shuns Hamas as a terrorist group. Hamas brushed off the U.S. diplomat’s appeal, saying it would not hold fire without making gains.

U.N. High Commissioner for Human Rights Navi Pillay said there was “a strong possibility” that Israel was committing war crimes in Gaza, where most Palestinian casualties have been civilians.

She also condemned indiscriminate Islamist rocket fire out of Gaza.

The U.N. Human Rights Council said it would launch an international inquiry into suspected violations.

Israel dismissed the threat. “Get lost,” Justice Minister Tzipi Livni said on her Facebook page in response to the investigation.

“Our interest and that of our people is that no agreement should be made before the conditions of factions of resistance are met,” Mr. Abu Zuhri said.

White House Deputy National Security Adviser Tony Blinken, meanwhile, said Hamas must be denied the ability to “rain down rockets on Israeli civilians.”

“One of the results, one would hope, of a cease-fire would be some form of demilitarization so that this doesn’t continue, doesn’t repeat itself,” Mr. Blinken said in an interview with NPR. “That needs to be the end result.”

On the ground, Israeli troops backed by tanks and aerial drones clashed with Hamas fighters armed with rocket-propelled grenades and assault rifles on the outskirts of Khan Younis, killing at least eight militants, a Palestinian health official said.

The Palestinian Red Crescent was trying to evacuate some 250 people from the area, which has been pummeled by airstrikes and tank shelling since early Wednesday.

As the battle unfolded, hundreds of eastern Khan Younis residents, many with children in tow, fled their homes and flooded into the streets with what few belongings they could carry. They said they were seeking shelter in U.N. schools.

“The airplanes and airstrikes are all around us,” said Aziza Msabah, a resident of Khan Younis. “They are hitting the houses, which are collapsing upon us.”

Farther north, in the Shijaiyah neighborhood of Gaza City, which endured intense fighting earlier this week, an airstrike demolished a home, killing 30-year-old journalist Abdul Rahman Abu Hean, his grandfather Hassan and his nephew Osama.

Israel launched its offensive July 8 to halt rocket salvos by Hamas and its allies, which have struggled under an Israeli-Egyptian economic blockade on Gaza and have been angered by a crackdown on their supporters in the West Bank.

After aerial and naval bombardment failed to quell the outgunned guerrillas, Israel poured ground forces into the Gaza Strip last Thursday, looking to knock out Hamas‘ rocket stores and destroy a vast network of tunnels.

“We are meeting resistance around the tunnels. They are constantly trying to attack us around and in the tunnels. That is the trend,” said Lt. Col. Peter Lerner, an Israeli military spokesman.

Israel said three of its soldiers were killed by explosive devices Wednesday, raising the army death toll to 32. Three civilians, including a Thai laborer hit Wednesday, have died in rocket attacks launched from Gaza.

The military said one of its soldiers is missing and believes he might be dead. Hamas said it has captured the soldier but has not released a picture of him in their control.

Clouds of black smoke hung over Gaza, some 40 miles south of Ben Gurion. The regular thud of artillery and tank shells filling the air drove out thousands of civilians in the town of Beit Hanoun in the northern Gaza Strip.

“This is not war; this is annihilation,” said 17-year-old Hamed Ayman. “I once dreamt of becoming a doctor. Today I am homeless. They should watch out for what I could become next.”

Palestinian medics said two worshippers were killed and 30 wounded in an attack on a mosque in the heart of the densely populated Zeitoun neighborhood in eastern Gaza City.

In southern Abassan and Khuzaa villages, residents said they were besieged by Israeli snipers who wounded two Palestinians as they tried to emerge from hiding with white flags in hand.

The Israeli army also seized Wafa hospital in eastern Gaza, saying it had been used to shelter Hamas fighters — a regular complaint from the military. The hospital removed patients after receiving warnings of the pending assault.

Israel named four commanders of the Islamic Jihad, a Hamas ally, that it said it had killed in recent days.

• This article is based in part on wire-service reports.

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