Ismail Haniya, the Hamas leader in Gaza, has said that peace would hold as long as cessation of "all Israeli aggression against the Palestinian people" is maintained.
Israel has said it will begin to ease its economic blocakde of Gaza on Sunday, should the truce hold.
Olmert will travel to Egypt on Tuesday to resume talks on a proposed prisoner swap with Hamas.
An Israeli military court has also ordered the release of Hamas politician Bassam al-Zahiri, who was detained two years ago.
'In the balance'
The UN agency for Palestinian refugees said on Thursday that it saw the truce as a "positive step" that could end months of delays to construction of schools, housing and medical centres desperately needed by the people of Gaza.
David Chater, Al Jazeera's correspondent in Israel, said: "The hopes of so many on both sides of the border now hang in the balance.
"Every minute, every hour that is now passing though is feeding the hopes of people that they can have a normal life."
Fighters from the Islamic Jihad organisation, one of the Palestinian factions who have signed up to the deal, were seen dismantling the rocket launchers used to strike Israeli towns across the border.
They removed the weapons from fields surrounding Beit Hanoun where in the past year hundreds, if not thousands, of rockets have been launched into southern Israel.
However, residents of the Gaza Strip and southern Israel were wary of putting too much faith in the deal.
"They make agreements and ceasefires here and there all the time. We will wait until we see real results," Hatem, a 30-year-old baker in Gaza City, said.
Nasser al-Farhan, a 22-year-old guard, said "God willing the period of calm will hold.
"But Israel has never kept to them before. It always continues with its attacks and its arrests."
Micha Hazan, 22, a café worker from the Israeli town of Sderot, close to the Gaza Strip, was just as sceptical: "They won't stop firing rockets until we send the tanks into Gaza, and even then, I'm not sure they would stop."
Ephi Levy, an Israeli farmer, said: "Let's hope it gets better with the tahadiya," he said, using the Arabic term for calm.
|Israeli settlers burnt a Palestinian olive tree field in the West bank on Thursday [AFP]
"The snipers kept shooting at us up until yesterday."
The ceasefire follows months of mediation by Egypt and is the first deal since Hamas seized power of the Gaza Strip from Fatah in June 2007.
However, concerns over the long-term risks of the deal remain.
Uzi Baron, a Sderot resident, told Al Jazeera that he feared that Hamas would use the peace "to manufacture more weapons and to smuggle".
While Roni Sofer, chief diplomatic correspondent for Israel's Ynet news service, said; "Israel has lost its ability to deter and remove a threat to its citizens. It allows a group that threatens it strategically to continue to exist.
"This is the agreement's biggest failure from Israel's standpoint."
West Bank settlements
Palestinians fear that the ceasefire will allow Israel to continue to expand illegal Jewish settlement activity in the occupied West Bank.
Jihad Hamad, a Gaza-based analyst, said: "The deal allows [Israel] to keep changing the facts on the ground, to build settlements and absorb more land from the West Bank."
There are additional fears that the peace deal may break down because it has not been extended to the West Bank.
Despite Palestinian calls for this extention, Israel refused. Israel says that its security forces must be able to work within the West Bank to combat Palestinian attacks.
Lamis Andoni, Al Jazeera's Middle East analyst, said: "Hamas was forced to accept the deal in the hope of easing the Israeli siege on Gaza and to alleviate Palestinian people's suffering.
"But the question remains will a truce hold if Israel conducts an operation in the West Bank that leads to Palestinian deaths? That will be a difficult challenge as individual fighters in Gaza could then be provoked into attacking Israeli posts."
The agreement states that if the ceasefire holds for three days Israel is obliged to increase fuel supplies to Gaza on Sunday. Israel has maintained a blockade on goods going into the Gaza Strip since Hamas took power.
Following that Hamas and Israel are expected to renew indirect talks in Cairo next week over a prisoner exchange.
Israel is seeking the release of Gilad Shalit, an Israeli soldier captured by Gazan fighters in a deadly cross border raid about two years ago, and will send an envoy of the prime minister to the talks.
The possible release of some of the more than 10,000 Palestinians held in Israeli jails will also be discussed.