* Temporary truce would start next week
* Israel wants to destroy tunnels, degrade militant capabilities
* Hamas wants an end to siege, open borders
* Egypt and Qatar key regional powers involved in talks
By Yasmine Saleh and Arshad Mohammed
CAIRO, July 24 (Reuters) - A possible truce to halt bloodshed in Gaza during the Muslim Eid al-Fitr holiday next week hinges on complex negotiations that have to give Hamas, Israel and regional powers a chance to claim political and military victories.
Egypt is trying to broker a temporary humanitarian truce which would start during one of Islam's biggest celebrations following the fasting month of Ramadan, in the hope that it will facilitate more permanent ceasefire talks.
Much depends on surmounting Arab rivalry. Egyptian President Abdel Fattah al-Sisi shares Israel hostility towards the Islamist Hamas that he too considers a terrorist group linked to the Egypt-based Muslim Brotherhood, which he toppled a year ago.
His biggest regional adversary and Muslim Brotherhood patron, the tiny Gulf state of Qatar, hosts Hamas leader Khaled Meshaal and is seen as essential to the success of talks.
Israel has killed more than 700 Palestinians in Gaza, mostly civilians, and wants to destroy more of the tunnels that enable Hamas' fighters to stage attacks inside Israel before it will accept any permanent ceasefire.
Among the central issues are whether Hamas may be willing to meet Israel's basic demand that it cease rocket fire into the Jewish state. The Islamists have their own list of demands.
Hamas, which with other Palestinian guerrillas has killed 32 Israeli soldiers inside Gaza and three civilians in Israel using rocket and mortars, wants to end a blockade imposed by Israel and Egypt, opening the Rafah crossing between Egypt and Gaza.
"The challenge now is to get everyone to agree on a deal that makes their side come out looking like the winner who crushed the other side," one senior Egyptian official said.
A "CLEAN" CEASEFIRE
U.S. Secretary of State John Kerry, in Cairo on Thursday for more talks with Egyptian mediators, has reported some progress in ceasefire talks as the fighting enters its third week.
"We have certainly made some steps forward. There is still work to be done," Kerry said on Wednesday.
U.S. officials have repeatedly said that they would like as "clean" a ceasefire agreement as possible - meaning one free of conditions such as easing the economic blockade of Gaza.
They say they can then begin negotiations on wider issues such as the reopening of the Rafah border crossing that has been closed for most of the year since the ousting of the Muslim Brotherhood in Cairo.
"The Israelis have talked a million times about demilitarization. You have heard Hamas say 'lift the siege of Gaza.' If you start trying to negotiate those issues before you have a ceasefire, those are incredibly complicated things to work through," a senior State Department official told reporter on Wednesday.
Yet with all sides wanting to exploit the pressure to end the violence, terms are being discussed and an unconditional ceasefire looks unlikely.
Hamas leader Khaled Meshaal said on Wednesday he supported a temporary truce to let humanitarian relief into Gaza but his group would keep fighting thereafter and would not agree to a more lasting ceasefire without a full negotiation of terms.
"Everyone wanted us to accept a ceasefire and then negotiate for our rights, we reject this and we reject it again today," he said at a news conference in Qatar.
Egypt is the official mediator but it does not talk directly to Hamas in Gaza, a policy which many blame for the breakdown of a first ceasefire on July 15.
Under former army chief Sisi, Egypt has tightened its stranglehold on the southern end of the Gaza Strip, intensifying an army operation to destroy tunnels to try to block supplies of weapons and prevent militants crossing.
An Egyptian army source said Cairo's position on Hamas has not changed: "We see them as a major threat, an offshoot of the Muslim Brotherhood group, lying right on our border.
"But we have an obligation to the Palestinian people," he said, signalling some softening of Egypt's approach to Hamas following an international outcry at Israel's attacks on Gaza.
Another senior Egyptian official said that despite Israeli unease, Israel trusted the new Egyptian authorities to watch the border closely and control weapons smuggling into.
Qatar has tolerated Egyptian mediation but has pushed for more representation for Hamas.
"Qatar has no problems with giving way to Egypt's new attempt to achieve a ceasefire, this is not a competition," a Qatar-based source familiar with the matter said.
"In order for any deal to be effective Hamas needs to take part because they are the ones on the ground in Gaza you simply can't exclude them because you disagree with their ideology."
Another core question is whether Israeli Prime Minister Benjamin Netanyahu feels he has sufficiently degraded Hamas' military capabilities to end the offensive launched this month.
Israel took action on July 8 to halt rocket salvoes by Hamas and its allies, triggered by a crackdown on their supporters in the nearby occupied West Bank after the kidnapping and killing of three Israeli teenagers from a Jewish settlement.
After aerial and naval bombardment failed to quell the outgunned guerrillas, ground forces poured into the Gaza Strip last Thursday.
Voices from Israel are least optimistic on a truce. Security cabinet minister Gilad Erdan said it would take at least another week to destroy the tunnels and Israel might have to do more.
"Eliminating and destroying the tunnels is something that will take another week to two weeks, and when the tunnel mission is over and if the rockets continue being fired here, then we will really face the dilemma of whether to deepen the incursion," he told Israel Radio on Wednesday.
The army says it has so far discovered 28 tunnels, roughly half of the network it believes Hamas has built.
Erdan indicated that Israel was willing to consider a pause in the fighting instead. "I think that a short humanitarian hiatus that does not harm the IDF (Israel Defence Forces) deployment and in which there is not talk of quitting the field is something that could be examined." (Additional reporting by Crispian Balmer in Jerusalem and Amena Bakr in Doha; Writing by Oliver Holmes; Editing by Paul Tayklor)