* New ceasefire holds hours after coming into effect
* Hamas says fired rockets at Tel Aviv minutes before truce
* Israeli negotiators expected in Cairo
* Israeli minister warns Gaza must be demilitarized
* U.N. hopes for durable ceasefire (Israeli negotiators heading to Cairo, Israeli minister remarks)
By Nidal al-Mughrabi and Ori Lewis
GAZA/JERUSALEM, Aug 11 (Reuters) - Israeli negotiators were due in Cairo on Monday for talks on ending a month-old Gaza war with Palestinian militants, an Israeli government official said, after a new 72-hour truce brokered by Egypt appeared to be holding.
The Israeli military said one rocket was launched at the Tel Aviv area, in Israel's commercial heartland, before the ceasefire went into effect at 2100 GMT on Sunday and may have landed in the sea. Hamas said it fired the missile.
A senior Israeli government official had said on Sunday Israeli negotiators would return to Cairo to resume indirect talks with the Palestinians only if the truce held.
A month of war has killed 1,910 Palestinians and 67 Israelis while devastating wide tracts of densely populated Gaza.
Gaza hospital officials say the Palestinian death toll has been mainly civilian since the July 8 launch of Israel's military campaign to quell Gaza rocket fire.
Israel has lost 64 soldiers and three civilians, while heavy losses among civilians and the destruction of thousands of homes in Gaza have drawn international condemnation.
The Israeli delegation to the Cairo talks had flown home on Friday when the sides failed to reach a deal to prolong a previous three-day truce.
A Hamas official said on Sunday Palestinian factions had accepted Egypt's call and that the Cairo talks would continue. Hamas spokesman Sami Abu Zuhri said that these new negotiations would be "the last chance" for a deal.
Hamas has demanded an end to Israeli and Egyptian blockades of the Gaza Strip and the opening of a seaport in the enclave - a project Israel says should be dealt with only in any future talks on a permanent peace deal with the Palestinians.
Egypt's Foreign Ministry urged "both sides to exploit this truce to resume indirect negotiations immediately and work towards a comprehensive and lasting ceasefire agreement".
Israeli Strategic Affairs Minister Yuval Steinitz said in a radio interview on Monday that disarming Gaza militants was crucial to sustain a long-term truce and he hoped this could be done by diplomacy rather than force.
"I certainly hope that there will be a diplomatic solution. If there will not be a diplomatic solution, I am convinced that sooner or later we will have to opt for a military solution of taking temporary control of Gaza to demilitarise it again," he told Israel Radio.
In Gaza, shops began to open and traffic was normal as displaced families returned to the homes they had been forced to abandon during Israeli attacks, expressing hopes that this truce would last after a series of failed ceasefires.
"God knows if it is permanent," said Abu Salama, a resident of Gaza's Shejaia district, as he and his family headed home on a donkey cart.
"A truce, no truce, it is becoming like Tom and Jerry. We want a solution," he said.
The new three-day ceasefire won praise from United Nations Secretary General Ban Ki-moon, who hoped it might lead to a durable ceasefire.
Israeli air strikes and shelling on Sunday killed nine Palestinians in Gaza, medics said, in a third day of renewed fighting since the last truce ended.
One air strike destroyed the home of Gaza City's mayor, Nezar Hijazi, across the street from the Reuters bureau where reporters and cameramen took cover as the explosion occurred. There were no casualties in the attack because Israel telephoned warnings to residents in the house and neighbouring buildings.
The Israeli military said it targeted 11 "terror squads" in Gaza, among them gunmen involved in or preparing to fire rockets.
Since the previous ceasefire expired, Palestinian rocket and mortar salvoes have focused on Israeli towns and communities near the Gaza frontier in what seemed a strategy of sapping morale without triggering another ground invasion of Gaza.
Residents of those communities, who had been assured by the military they could return home when last week's truce began, have accused Israeli authorities of misleading them.
The violence of the past three days has been less intense than at the war's outset, with reduced firing on both sides, raising hopes the conflict could be nearing its end.
In the talks that convened in Cairo earlier this month, Egypt has been meeting separately with each party, as neither recognises the other. Hamas rejects Israel's right to exist and Israel shuns Hamas as a terrorist organisation.
Another sticking points in their talks has been Israel's demand for guarantees that Hamas would not use any reconstruction supplies sent to Gaza to build tunnels of the sort Palestinian fighters have used to infiltrate Israel.
Hamas has demanded an end to the economically stifling blockade of the enclave imposed by both Israel and Egypt, which also sees the Islamist movement as a security threat.
Israel has resisted easing access to Gaza, suspecting Hamas could then restock with weapons from abroad.
Israeli tanks and infantry left the enclave on Tuesday after the army said it had completed its main mission of destroying more than 30 tunnels dug by militants for cross-border attacks.
(Writing by Allyn Fisher-Ilan; Editing by Eric Walsh, Clarence Fernandez and Giles Elgood)