(Edits throughout, adds detail, background)

By Alastair Macdonald

JERUSALEM, June 22 (Reuters) - Envoys for international powers trying to mediate a peace in the Middle East agreed on Friday to talk in Jerusalem next week, a day after the first meeting in two months between Israeli and Palestinian leaders.

A week after Islamist militias wrenched control of the Gaza Strip from the secular Fatah forces of Western-backed President Mahmoud Abbas, leaders across the region and beyond are still digesting the implications of the Palestinians' schism for the prospects of establishing a state and making peace with Israel.

Envoys of the Quartet -- the United States, European Union, United Nations and Russia -- will have their chance to do so on Tuesday, Israel and diplomats said. The day before, Abbas will meet Israeli Prime Minister Ehud Olmert at Sharm el-Sheikh in Egypt in a four-way summit with the leaders of Egypt and Jordan.

Both sides have spoken of Abbas's break with Hamas in Gaza as a "new beginning" after a chill that set in last year when the Islamists, who refuse to renounce violence or recognise Israel, won a parliamentary election and formed a government.

But as both Israel and Abbas's new emergency cabinet in the West Bank turn the screws of an embargo on Hamas, prompting U.N. aid chiefs to warn of a "major humanitarian crisis" in Gaza, many question whether either leader has the support at home to deliver what the other wants to reopen serious negotiations.

Olmert, whose popularity ratings have been in single digits since Israel's war in Lebanon a year ago, said on Thursday he expected full support from U.S. President George W. Bush, who told him in Washington this week that he still wanted to see a Palestinian state founded before he leaves office in 18 months.

Abbas's negotiator Saeb Erekat told Reuters on Friday: "The most important thing is that we revive a meaningful peace process that leads to implementing President Bush's vision.

"We hope the Israelis take this chance seriously ... This summit is not for negotiations ... It's time for decisions."

SCEPTICISM

However, senior officials on both sides made no secret of their scepticism on any breakthrough, particularly since Gaza, home to a third of the four million population of the proposed state, is controlled by leaders hostile to Abbas and Israel.

"Gaza is isolated not only from Israel but first of all from the Palestinians themselves," Israeli Infrastructure Minister Benjamin Ben-Eliezer said. "I don't even dream of seeing a peace process very soon. I dream only of seeing a bit of quiet."

Decisions by Washington, Brussels and Israel to lift their sanctions on the Palestinian Authority in the occupied West Bank while tightening restrictions on Hamas in Gaza have done little to improve trust between Abbas's administration and Israel.

"Israel is releasing money not because they are honourable but they want to entrench the divide between the West Bank and Gaza," Abbas security aide Mohammad Dahlan said this week. He dismissed talk of real peace: "There is no political horizon."

Abbas fired another top security official, Rashid Abu Shbak on Friday, possibly over the rout in Gaza.

Israel's release of some of the $700 million in Palestinian tax revenue, collected by Israeli officials over the past year, is expected to be approved by Olmert's cabinet on Sunday.

The payment may be about $400 million, diplomats and Israeli officials said -- a shortfall the Palestinians say is not acceptable. Abbas's demands for a sweeping removal of Israeli military checkpoints across the West Bank and for more heavy weaponry for his security forces to enforce a new ban on militias are also likely to be disappointed, Israeli political sources said.

Israel places little faith in Abbas's order this week outlawing all but official armed groups and officials say they fear that, as in Gaza, new weapons could fall into Hamas hands.

A war of words between the two Palestinian factions has also heated up. Hamas on Friday presented what it said was evidence from captured Fatah documents of orders for "ethnic cleansing" of their supporters and of "collaboration" with Israel.

It denied Abbas's accusation that Hamas tried to blow him up and said Dahlan's security men secretly filmed Fatah officials in "sexual situations" in order to ensure their loyalty.

Many in Gaza, including Hamas officials, are concerned not to be isolated, as supplies run low behind Israel's cordon:

"We call on President Mahmoud Abbas to work in the general interest," the preacher at one big Gaza mosque told worshippers in his weekly sermon. "There are families who are starving to death, and there are sick people facing death."

(Additional reporting by Adam Entous and Allyn Fisher-Ilan in Jerusalem, Mohammed Assadi in Ramallah and Nidal al-Mughrabi in Gaza)

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