* New ceasefire holds hours after coming into effect
* Hamas says fired rockets at Tel Aviv minutes before truce
* Israelis, Palestinians begin indirect talks in Cairo
* Israeli minister warns Gaza must be demilitarized
* U.N. hopes for durable ceasefire
By Nidal al-Mughrabi and Ori Lewis
GAZA/JERUSALEM, Aug 11 (Reuters) - Israeli and Palestinian negotiators resumed indirect talks mediated by Egypt on Monday on ending a month-old Gaza war, Egypt's state news agency said, after a new 72-hour truce 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 began at 2100 GMT on Sunday and may have landed in the sea. Gaza's dominant Hamas group said it fired the missile.
A senior Israeli government official had said on Sunday Israeli negotiators, who had left Cairo on Friday hours before a previous three-day ceasefire expired, would return to Egypt to resume the talks only if the new truce held.
Hamas is demanding 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.
A month of war has killed 1,938 Palestinians and 67 Israelis while devastating wide tracts of densely populated Gaza, and Egypt's Foreign Ministry has urged both sides to work towards "a comprehensive and lasting ceasefire agreement".
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.
Hamas spokesman Sami Abu Zuhri said the new negotiations would be "the last chance" for an agreement. Israeli representatives are not meeting face-to-face with the Palestinian delegation because it includes Hamas, which Israel regards as a terrorist organisation.
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.
Another sticking points in the Cairo 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.
According to the United Nations, at least 425,000 displaced people in the Gaza Strip are in emergency shelters or staying with host families. Nearly 12,000 homes have been destroyed or severely damaged by Israeli attacks.
In Gaza, shops began to open and traffic was normal as some 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.
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.
Four wounded Palestinians were flown into Ankara for medical treatment on Monday, the first sign of Turkey's promised plan to evacuate thousands from the Gaza Strip.
A Turkish aid group said it would send ships again to challenge the Israeli blockade of Gaza, four years after Israeli commandos stormed its flotilla bound for the Palestinian territory and killed 10 people in fighting with activists on board.
(Writing by Allyn Fisher-Ilan; Editing by Eric Walsh, Clarence Fernandez and Giles Elgood)