* Under Egyptian proposal, both sides hold fire from 0500 GMT
* Israeli envoys due in Cairo to negotiate more enduring deal
* Ground forces quit Gaza, having razed 32 infiltrator tunnels
* Palestinian death toll 1,834; 67 killed on the Israeli side
By Nidal al-Mughrabi, Lin Noueihed and Dan Williams
GAZA/CAIRO/JERUSALEM, Aug 5 (Reuters) - Israel and Hamas-led Palestinian guerrillas entered a 72-hour truce on Tuesday mediated by Egypt with a view to encouraging negotiations on a more enduring end to the month-old Gaza war.
Minutes before the ceasefire took hold at 8 a.m. (0500 GMT), Hamas launched a salvo of long-range rockets, calling them revenge for Israel's "massacres". Sirens went off as far north as Jerusalem's outlying areas. There was no word of casualties.
Israeli ground forces withdrew from the Gaza Strip ahead of the truce, with a military spokesman saying their main goal of destroying cross-border infiltration tunnels had been completed.
Troops and tanks would be "redeployed in defensive positions outside the Gaza Strip and we will maintain those defensive positions," spokesman Lieutenant-Colonel Peter Lerner said, reflecting Israeli readiness to resume fighting if attacked.
Several previous attempts by Egypt and other regional powers, overseen by the United States and United Nations, failed to calm the worst Israeli-Palestinian fighting in two years.
Gaza officials say the war has killed 1,834 Palestinians, most of them civilians. Israel says 64 of its soldiers and three civilians have been killed since fighting began on July 8, after a surge in Palestinian rocket launches.
Israel was expected to send delegates to join talks in Cairo to cement a longer-term deal during the course of the truce.
For now, Strategic Affairs Minister Yuval Steinitz told Israel's Army Radio: "There are no agreements. As we have already said, quiet will be answered with quiet."
Hamas spokesman Sami Abu Zuhri said the Islamist group had also informed Egypt "of its acceptance of a 72-hour period of calm," beginning on Tuesday.
The U.S. State Department praised the truce and urged the parties to "respect it completely". Spokeswoman Jen Psaki added that Washington would continue its efforts to help the sides achieve a "durable, sustainable solution for the long term".
Efforts to cement the ceasefire into a lasting truce could prove difficult, with the sides far apart on key demands, and each rejecting the other's legitimacy. Hamas rejects Israel's existence, and vows to destroy it, while Israel denounces Hamas as a terrorist group and eschews any ties.
Besides the truce, Palestinians demand an end to the Israeli-Egyptian blockade on impoverished Gaza and the release of prisoners including those Israel arrested in a June crackdown in the occupied West Bank after three Jewish seminary students were kidnapped and killed.
Israel has resisted those demands in the past.
ISRAEL: DEMILITARISE GAZA
Lerner said the army overnight destroyed the last of 32 tunnels located inside Gaza and which had been dug by Hamas for cross-border attacks at an estimated cost of $100 million.
"Today we completed the removal of this threat," he said.
Israeli officials say, however, that some tunnels may have gone undetected and that the armed forces are poised to strike at these in the future.
Prime Minister Benjamin Netanyahu also wants to disarm Hamas and demilitarise Gaza, stripping of their arsenals guerrillas who launched more than 3,300 rockets and mortar bombs at Israel this past month. Hamas has ruled that out.
"For Israel the most important issue is the issue of demilitarisation. We must prevent Hamas from rearming, we must demilitarise the Gaza Strip," Netanyahu spokesman Mark Regev told Reuters television.
Since the fighting began, several previous truces barely held. Regev said Israel had accepted Egypt's terms weeks before Hamas, and expressed a wish that the truce would last: "I hope this time we see the ceasefire work that's good for everybody."
Egypt has positioned itself as a mediator in successive Gaza conflicts but, like Israel, its current administration views Hamas as a security threat.
Besides the loss of life, the war has cost both sides economically. Gaza faces a massive $6-billion price tag to rebuild devastated infrastructure. Israel has lost hundreds of millions of dollars in tourism, other industry, and fears cuts in overall economic growth this year as well.
In northern Gaza, some of the hundreds of thousands of Palestinians displaced by the fighting cautiously headed back to their battered towns. A column of evacuees trundled into northern Beit Hanoun in donkey-drawn carts.
The violence had shown signs of abating early on Tuesday, with few reported incidents. Two rockets were fired at a southern Israeli city, Ashkelon, and Israel's Iron Dome interceptor shot them down. There were no casualties.
On Monday, Palestinians accused Israel of bombing a refugee camp in Gaza City, killing an eight-year-old girl and wounding 29 people in a disruption of what was supposed to have been a seven-hour humanitarian ceasefire.
A military spokeswoman disputed this, saying Israel had withheld aerial fire for seven hours on Monday, in a move to free up aid supplies and allow some of the hundreds of thousands of Palestinians displaced by the war to go home.
Media in Britain reported that a British aid worker was killed on Sunday during an Israeli strike in Rafah while he was delivering supplies to a hospital. The British Foreign Office said it was looking into the report. (Additional reporting by Eric Beech in Washington, Ori Lewis in Jerusalem, Yasmine Saleh in Cairo; Writing by Allyn Fisher-Ilan; Editing by Ken Wills and Robert Birsel)