* American, European flights expected back in Tel Aviv
* Kerry reports truce progress; Israel wants more time
* Hamas sticks to demand embargo on enclave be lifted (Updates toll, adds European flight advisory)
By Nidal al-Mughrabi and Dan Williams
GAZA/JERUSALEM, July 24 (Reuters) - Israel won a partial reprieve from the economic pain of its Gaza war on Thursday with the lifting of a U.S. ban on commercial flights to Tel Aviv, as fighting pushed the Palestinian death toll over 700.
A truce between the Jewish state and Hamas-led Islamist guerrillas remained elusive despite intensive mediation bids.
Palestinians said residents of two southern villages were trapped by days of tank shelling, with medics unable to evacuate wounded. U.N. agencies said more than 140,000 people had been displaced. Hamas fired rockets at Tel Aviv and said its gunmen carried out a lethal ambush on Israeli soldiers in north Gaza.
With Washington's encouragement, and the involvement of Turkey and Hamas ally Qatar, Egypt has been trying to broker a limited humanitarian ceasefire for the battered enclave.
One Cairo official said on Wednesday it could take effect by the weekend, in time for the Eid al-Fitr festival next Monday or Tuesday, Islam's biggest annual celebration at the end of the fasting month of Ramadan.
But a U.S. official described any truce by the weekend as unlikely, as did an Israeli security cabinet minister who said the army would need one to two weeks to complete its main mission of razing tunnels used by Hamas for cross-border raids.
"If the talk is of a humanitarian hiatus for - this is not pleasant to say - removing bodies, all kinds of things that are connected to the civilian population in the short-term, this might be weighed," the minister, Gilad Erdan, told Israel Radio.
"But I will oppose any ceasefire until it is clear both that the tunnels will be destroyed and what will happen in the post-ceasefire period - how we will guarantee that quiet for the residents of Israel will really be preserved in the long-term."
The death toll in Gaza reached 729 on Thursday as Israeli tank fire and pre-dawn assaults killed 35 people in the Hamas-dominated coastal enclave, including an 18-month-old baby and six members of the same family, Palestinian officials said.
In southern Khuzaa and Abassan villages, they said, Israeli shelling left dead and wounded under rubble, while medical crews could not risk approaching. Elsewhere in Gaza, a U.N. aid agency said three of its teachers were killed in Israeli air strikes.
Israel has lost at least 32 soldiers in clashes inside Gaza and with Hamas raiders who have slipped across the fortified frontier in tunnels. The military confirmed there had been a new clash on Thursday but did not immediately publish casualties.
Palestinian rockets and mortar bombs have killed three civilians in Israel. Such shelling surged last month as Israel cracked down on Hamas in the occupied West Bank, triggering the July 8 air and sea barrage on the Gaza Strip that escalated into an invasion a week ago.
Though Israel's Iron Dome rocket interceptor has shot down most of the rockets fired from Gaza, one that came close to Tel Aviv's Ben Gurion Airport on Tuesday prompted the U.S. Federal Aviation Administration (FAA) to bar American flights there.
An ensuing wave of cancellations by foreign airlines emptied Israel's usually bustling international gateway and hurt its hi-tech economy at the height of summer tourist season. It was hailed as a victory by Hamas and prompted Israeli Prime Minister Benjamin Netanyahu to appeal to the Obama administration to intervene.
The FAA cancelled the ban late on Wednesday after reviewing the security situation. The European Air Safety Agency (EASA) said on Thursday it was about to follow suit and lift its own recommendation to avoid flying to Tel Aviv.
US Airways, a unit of American Airlines Group Inc, said it was resuming its non-stop Tel Aviv to Philadelphia service. Germany's Lufthansa said its suspension of flights to Tel Aviv would continue to Friday.
"The Europeans did not really deliberate over this, but acted more as a follow-up to the American decision," said Gadi Regev, chief of staff for Israel's Civil Aviation Authority.
Some European flights have been diverted to Cyprus's Larnaca airport, where passengers took Israeli carriers to Ben Gurion.
In what appeared to be an attempt to trigger a fresh FAA ban, Hamas said it launched at least two rockets at Ben Gurion on Thursday. But no sirens were heard at the airport as the rockets flew wide and were shot down by Iron Dome over Tel Aviv, to the west, and Petah Tikva, to the north.
Hamas leader Khaled Meshaal said his fighters had made gains against Israel and voiced support for a humanitarian truce, but only if Israel eased restrictions on Gaza's 1.8 million people. Hamas wants next-door Egypt to open up its border with Gaza too.
"Let's agree first on the demands and on implementing them, and then we can agree on the zero hour for a ceasefire," Meshaal said on Wednesday in Qatar. "We will not accept any proposal that does not lift the blockade ... We do not desire war and we do not want it to continue, but we will not be broken by it."
U.N. High Commissioner for Human Rights Navi Pillay said there was "a strong possibility" that Israel was committing war crimes in Gaza, where medical officials say most of those killed were civilians.
Pillay also condemned indiscriminate Islamist rocket fire out of Gaza, and the U.N. Human Rights Council said it would launch an international inquiry into alleged violations.
A furious Netanyahu denounced the inquiry as a "travesty".
"The HRC should be launching an investigation into Hamas's decision to turn hospitals into military command centres, use schools as weapons depots and place missile batteries next to playgrounds, private homes and mosques," he said.
U.N. Secretary-General Ban Ki-moon, who has also been on a truce-seeking mission, lashed out at Gaza militants, expressing "outrage and regret" that rockets had been found inside a U.N. school for refugees for the second time during the conflict.
Ban said storing rockets there "turned schools into potentially military targets, endangering the lives of innocent children", along with U.N. employees and the tens of thousands of sheltering Palestinians. He urged an investigation.
U.S. Secretary of State John Kerry returned to Egypt on Wednesday after seeing Palestinian President Mahmoud Abbas in the occupied West Bank and Ban and Netanyahu in Jerusalem.
"We have certainly made some steps forward. There is still work to be done," said Kerry, on one of his busiest regional visits since Netanyahu called off U.S.-sponsored peace talks over Abbas's power-share deal with Hamas in April.
Gaza has been rocked by regular bouts of violence since Israel unilaterally pulled out of the territory in 2005.
Hamas, which rejects Israel's right to exist and is shunned in the West, balked at Egypt's proposal for an unconditional truce, saying its terms had to be met in full for any end to the conflict. Israel briefly held fire last week at Cairo's behest.
The war is exacting a heavy toll on impoverished Gaza. Officials say at least 475 houses have been destroyed by Israeli fire and 2,644 damaged. Some 46 schools, 56 mosques and seven hospitals have also suffered varying degrees of damage.
Israel says one of its soldiers is missing in Gaza, and the military believes he might be dead. Hamas says it has captured him but has not released a picture of him in their hands. (Additional reporting by Noah Browning in Gaza, Arshad Mohammed and Yasmine Saleh in Cairo, Amena Bakr in Doha, Stephanie Nebehay in Geneva, and Thomas Seythal in Berlin; Writing by Dan Williams; Editing by Nick Macfie and Paul Taylor)