Ehud Barak, Israel's defence minister, said it was too early to talk about a truce and that details of any deal were still being finalised.
"It's early to herald a ceasefire, and even if it were to happen ... it is difficult to estimate how long it will last," he said in Tel Aviv on Tuesday.
"The test will be in the implementation, but it is important to give it a chance."
David Chater, Al Jazeera's correspondent in Jerusalem, said a senior Israeli delegation was travelling to Egypt on Tuesday night to meet Egyptian intelligence chief, Omar Suleiman, who is brokering the deal.
But Hossam Zaki, Egypt's foreign ministry spokesman, told Al Jazeera that the quiet confirmation of the deal is as official as the ceasefire announcement will get.
"We had problems in the course of the negotiations because one party didn't recognise the other. In fact, they both don't recognise each other, so we wanted to skip the issue of a formal announcement," he said.
"Both sides have pledged to halt all hostilities and all military activities against each other ... [But] what is said by both sides is not important; what is important is the implementation."
Mark Regev, a spokesman for Ehud Olmert, the Israeli prime minister, said last week that Israel would continue preparations for broad military action as a matter of national security.
"What is important is not words but actions," he said, repeating Israel's demands for an end to attacks on Israeli civilians, a halt to arms smuggling into the Gaza Strip, and progress towards the release of Corporal Gilad Shalit, an Israeli soldier seized by Gaza fighters two years ago.
Hamas have pushed for the release of about 450 Palestinians from Israeli jails, but this demand is not thought to be included in the deal.
Khalil al-Haya, a Hamas leader, speaking at a news conference in Gaza on Tuesday, said that Egypt will seek to extend the truce into the West Bank.
Timeline: Ceasefire efforts
June 17, 2008: Truce announced between Israel and Gaza's Hamas government, to take effect from June 19
June 11, 2008: Israel's security cabinet backs Egypt's truce efforts but says army has been instructed to prepare for possible Gaza offensive if mediation fails
March 4, 2008: Egypt calls for ceasefire between Hamas and Israel
January 23, 2007: The Rafah border wall is blown up and tens of thousands of Palestinians pour into Egypt from Gaza to shop for food and fuel in short supply because of the Israeli-led blockade. The border is sealed again a few days later
November 27, 2007: US hosts a peace conference, eliciting promises from Israel and the Palestinians to try to forge a two-state agreement before end of 2008
June 14, 2007: Hamas seizes Gaza after overpowering Fatah forces in a week of fighting in which killed at least 100 people. Abbas later dismisses Hamas-led unity government and appoints a Fatah-backed administration. Israel tightens a blockade of Gaza
Egyptian authorities will hold a meeting with Hamas and the Palestinian Authority a week after the end of the truce in order to open the Rafah crossing with Egypt, al-Haya said.
"We respect the terms of the truce, and in case of any problems, we will seek Egypt's help," he said.
Asked what Hamas would do if Israel breaches the truce, Mahmoud al-Zahar, a senior Hamas politician, said: "I don't think that the Israelis now plan to breach the agreement, however, should this take place, we will defend our people."
Reacting to the news of the truce, Tom Casey, a US state department spokesman, said that Washington would "love to see Hamas get out of the terrorist business" and "be participants in the political process".
"But saying you've got a loaded gun to my head and you're not going to fire it - as Hamas did today - is very different to locking the gun away completely," he said.
"It hardly meets the terms that the Quartet has laid out, nor those of [Palestinian] President [Mahmoud] Abbas for the reincorporation of Hamas into the Palestinian political process."
Ayman Mohyeldin, Al Jazeera's correspondent in Gaza, said that Hamas is confident that the ceasefire deal is workable.
"The military in Gaza, which comes under Hamas jursidiction, would be able to halt and suspend all rockets into southern Israel, and stop any further attacks.
"There is also the belief that the border crossing deal [will] come into play - allowing necessary fuel back into the territory and therefore reducing power cuts. It will allow a sense of normalcy to resume here.
Mohyeldin quoted a Hamas official as telling him that they do not want to be held responsible for all Palestinian factions in the territory.
"As a result, Egypt, in their mediation efforts, presented the ceasefire conditions to all Palestinian factions so that all those who accept the ceasefire will have to abide by its conditions," he said.