* PLO endorsement could help Cairo's truce bid
* Israel presses offensive, Gaza toll hits 624
* Slain officer brings Israeli losses to 31
* Foreign airlines shun Tel Aviv over rocket risk (Updates Israeli death toll)
By Nidal al-Mughrabi and Dan Williams
GAZA/JERUSALEM, July 23 (Reuters) - The Palestinian decision-making body led by U.S.-backed President Mahmoud Abbas on Wednesday endorsed demands by Hamas for halting Gaza hostilities with Israel, a closing of ranks that may help Egyptian-mediated truce efforts.
With Israeli and U.S. encouragement, Egypt has tried to get both sides to hold fire and then negotiate terms for protracted calm in the Palestinian enclave where officials said 624 people, mostly civilians, have been killed in 15 days of fighting.
Hamas, the Gaza Strip's dominant Islamists, and other armed factions had balked at Cairo's offer, saying they wanted assurances of relief from an Israeli-Egyptian blockade and other concessions. The dispute was further complicated by distrust between Egypt under President Abdel Fattah al-Sisi and Hamas.
In a move that could effectively turn Abbas into the main interlocutor for a Gaza truce, his umbrella Palestine Liberation Organization (PLO) on Wednesday formally supported core conditions set by the Hamas-led fighters.
"The Gaza demands of stopping the aggression and lifting the blockade in all its forms are the demands of the entire Palestinian people and they represent the goal that the Palestinian leadership has dedicated all its power to achieve," senior PLO official Yasser Abed Rabbo said in Ramallah, the hub city in the Israeli-occupied West Bank where Abbas is based.
"We are confident Gaza will not be broken as long as our people are standing beside it to support it through all possible means until the invaders understand that our great people inside the homeland and outside will not leave Gaza alone."
Signaling that Abbas, too, sought a staggered cessation of hostilities, the Palestinian leader's Fatah faction on Tuesday proposed a truce followed by five days of negotiations on terms.
There was no immediate response to the PLO statement from Hamas or Israel, which pressed the Gaza offensive it began on July 8 after a surge of cross-border rocket salvoes.
VIOLENCE AFFECTS FLIGHTS
Israel has lost 29 soldiers in the Gaza clashes, including a tank officer who the army said on Wednesday had been killed by a Palestinian sniper overnight. Two Israeli civilians have been killed by shelling by Palestinian fighters that has reached deep into the Jewish state, spreading panic despite the success of its Iron Dome rocket interceptor and civilian shelters.
Three Palestinians died in Israeli strikes on Wednesday, Gaza officials said. Rocket launches set off air-raid sirens in southern Israel, but there was no word of casualties.
There was also violence in the West Bank, where a Palestinian was shot dead by Israeli troops near Bethlehem. The army said soldiers fired a rubber bullet at him during a confrontation with dozens of Palestinians hurling rocks and Molotov cocktails.
Egyptian sources, speaking on Tuesday as U.S. Secretary of State John Kerry visited Cairo to advance truce efforts, said a unified Palestinian position could help achieve a deal.
Unlike Hamas, which refuses permanent coexistence with the Jewish state, the PLO has pursued peacemaking for two decades.
Those efforts were set back in April when Israeli Prime Minister Benjamin Netanyahu called off U.S.-sponsored peace negotiations over Abbas's surprise power-share deal with Hamas.
Yet Netanyahu stopped short of cutting ties with Abbas, whose forces help secure the West Bank, and foreign mediators continue to see the Palestinian leader as someone the Israelis can negotiate with.
Having unilaterally accepted an Egyptian-proposed truce last week that was rejected by Hamas, the Israelis made clear on Tuesday they would not stand down before their forces destroyed Hamas's military infrastructure, including rocket sites and a network of tunnels used for cross-border Palestinian raids.
"A cease-fire is not near," said Justice Minister Tzipi Livni, the most dovish member of Netanyahu's security cabinet.
Yet Israel faced mounting international alarm at the toll on Palestinian civilians, as well as economic pressure from lost tourism that soared on Tuesday when the U.S. Federal Aviation Administration (FAA) took the rare step of banning flights to Tel Aviv's Ben-Gurion International Airport for at least 24 hours after a rocket from Gaza struck nearby, wounding two people.
European airlines also canceled flights to Israel, whose own carriers continued to operate.
An Israeli official said Netanyahu asked Kerry to help restore the U.S. flights. A U.S. official said the Obama administration would not "overrule the FAA" on a security precaution but noted the ban would be reviewed after 24 hours.
FOCUS ON HAMAS
Following meetings in Egypt, which has some leverage over Hamas through its control of its border with Gaza, Kerry said on Tuesday there was still "work to do" to resolve the conflict and urged the Palestinian Islamists to pursue negotiations.
Because Washington, like Israel and the European Union, deems Hamas a terrorist group, they have no direct contact and Washington must rely on proxies such as Egypt, Qatar and Turkey.
In a sign of the intensity of the U.S. diplomacy, Kerry spoke to Netanyahu and to Qatari and Turkish foreign ministers after meeting Sisi for two hours, a senior U.S. official said.
"The Egyptians have provided a framework and a forum for them to be able to come to the table to have a serious discussion together with other factions of the Palestinians," Kerry said. "Hamas has a fundamental choice to make and it is a choice that will have a profound impact for the people of Gaza."
Angered by an Israeli crackdown on its supporters in the West Bank and by Gaza's hardship under blockade, Hamas has said it is willing to continue fighting. In addition to freeing up Gaza's borders, Hamas wants a prisoner release by Israel.
The Egyptian plan does not specify a timeline for easing the blockade, saying "crossings shall be opened and the passage of persons and goods through border crossings shall be facilitated once the security situation becomes stable on the ground".
U.S. officials view Qatar, a tiny, gas-rich Gulf state that has supported Hamas financially and hosts some of the militant group's senior leaders, as important to the diplomacy.
In contrast, the Egyptian government is deeply suspicious of Hamas as it is an offshoot of the Muslim Brotherhood movement toppled from power in Cairo by then-army chief Sisi last year.
Israel is openly opposed to giving Qatar or Turkey leading roles in mediation, given its troubled ties with both countries.
The upcoming Eid al-Fitr festival - Islam's biggest annual celebration that follows the end of the fasting month of Ramadan this weekend - could provide all sides with a convenient moment to agree to a cease-fire.
Asked about Eid, a senior Obama administration official said: "It's a potential opportunity. We want there to be a cease-fire as soon as possible basically, and insofar as that's a marker that can compel Hamas to the table that would be a good thing, but the bottom line is they're going to have to stop firing rockets." (Additional reporting by Arshad Mohammed in Cairo and Amena Bakr in Doha; Writing by Dan Williams; Editing by Ken Wills and Ron Popeski)