Washington’s top diplomat said global efforts to end 16 days of conflict in Gaza were progressing Wednesday as the fighting raged on and airlines suspended flights over rocket fears.

As US Secretary of State John Kerry and UN chief Ban Ki-moon held talks in Jerusalem, they appeared cautiously optimistic, saying they had pooled their efforts in the hope of boosting the quest for a truce in a conflict that has claimed the lives of 678 in Gaza, according to Palestinian sources in the Hamas-run enclave, and 34 Israelis.

Israel launched Operation Protective Edge in a bid to stem Gazan rocket fire upon its civilians, and find and destroy cross-border tunnels through which Hamas gunmen have attempted to launch terrorist attacks.

“We have certainly made some steps forward, but there is still work to be done,” Kerry said as he met the UN chief for the second time this week.

“We are now joining our forces in strength to make a ceasefire as soon as possible,” Ban said, warning there was no time to lose as concern mounted over the rising civilian body count.

The US diplomat offered a similar message to the Palestinians.

“We have in the last 24 hours made some progress in moving toward that goal,” Kerry said after meeting Palestinian president Mahmoud Abbas in the West Bank city of Ramallah, before heading to Tel Aviv for talks with Israeli Prime Minister Benjamin Netanyahu.

Palestinians inspect the destruction in Farouq Mosque after it was hit in an Israeli airstrike, in Rafah, southern Gaza Strip on July 22, 2014. (photo credit: Abed Rahim Khatib/Flash90)

Palestinians inspect the destruction in Farouq Mosque after it was hit in an Israeli airstrike, in Rafah, southern Gaza Strip on July 22, 2014. (photo credit: Abed Rahim Khatib/Flash90)

Britain’s new Foreign Secretary Philip Hammond was also expected in the region later on Wednesday for late-night talks with Abbas, the president’s office said.

But neither Israel nor Hamas showed any indication of being ready to cease fire, despite days of diplomatic efforts to coax them into a truce.

Palestinian health officials said more than 27 people were killed on Wednesday.

Most of Wednesday’s dead were in Khuzaa on the Israeli border, close to the southern city of Khan Yunis, the scene of very heavy fighting since before dawn.

In Israel, the army confirmed five more soldiers had died in fighting on Tuesday.

Police said a foreign worker had been killed when a rocket fired from Gaza struck the greenhouse where he was working in southern Israel. They did not specify his nationality.

On the ground, the fighting was briefly suspended in several flash-point areas to allow ambulances to retrieve the wounded, a spokeswoman for the International Committee of the Red Cross said.

She said seven ambulances had entered Shejaiya near Gaza City and another nine ambulances had entered Khuzaa, while a third convoy had entered Beit Hanun in the north.

Parents, siblings and friends of IDF lone soldier Max Steinberg, killed in Gaza, follow his coffin to the burial on Mount Herzl on Wednesday morning, June 23 (photo credit: Miriam Alster/Flash 90)

Parents, siblings and friends of IDF lone soldier Max Steinberg, killed in Gaza, follow his coffin to the burial on Mount Herzl on Wednesday morning, June 23 (photo credit: Miriam Alster/Flash 90)

In Gaza City, hundreds of people, mostly women and children, packed into the pews of Saint Prophyrios Greek Orthodox church seeking shelter from the violence outside.

“Many of them, their houses are destroyed. Many people have been injured or killed. So we try to help these people,” said Archbishop Alexios, one of Gaza’s tiny community of 1,500 Christians.

Kerry’s arrival in Tel Aviv came a day after a Gaza rocket struck close to the airport, prompting the US Federal Aviation Authority to ban commercial flights to and from Israel for at least 24 hours.

And its European counterpart advised all carriers to avoid Tel Aviv “until further notice” in a moved mirrored Wednesday by Royal Jordanian and Turkish Airlines.

Netanyahu appealed to Kerry to lift the ban, the first since the 1990-1991 Gulf War, with the US diplomat assuring him it would be reviewed within a day.

Kerry began his regional mission in Cairo, discussing ceasefire proposals with Egyptian President Abdel Fattah el-Sissi, that he said provided a “framework” to end the fighting.

An initial Egyptian proposal calling for a halt to hostilities ahead of talks was accepted by Israel early last week but rejected by Hamas, which wants agreement on a comprehensive package before holding its fire.

As the violence raged on, UN rights chief Navi Pillay condemned both Israel and Hamas at an emergency session of the UN Human Rights Council in Geneva.

She said Israeli attacks which had killed civilians, among them children, could amount to war crimes.

“There seems to be a strong possibility that international law has been violated, in a manner that could amount to war crimes,” Pillay said.

She also denounced Hamas for its “indiscriminate attacks” on Israeli civilians.