"We cannot trust Israel because I think Israel is not interested in a truce or ceasefire ... but here in Gaza I think that all Palestinian factions are together, and I think of all of them expressed their respect and that they want to be committed to the ceasefire," he said.
On Israel's part, government spokesman Mark Regev questioned whether Hamas would respect the ceasefire.
"We have to see that this isn't a calm that is used by the terrorist in Gaza as a timeout, that they just use this to rearm and group," he told Al Jazeera.
"I think everyone is looking at Hamas, are they really serious about this?" he asked. "Their track record is one of continued violence, terrorism and murder."
If the ceasefire deal lasts for three days, Israel will ease its blockade on Gaza, allowing vital supplies into the territory.
Should the truce hold after that, it will lead to talks on opening the Rafah crossing between Gaza and Egypt.
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
It is unclear if the deal involves any type of prisoner exchange.
Egypt opened its border with the Gaza Strip on Wednesday, a security official said, to allow Palestinians to return to the territory after receiving medical treatment.
The official said the opening of the border crossing was "exceptional", and was only done so that sick Gazans could return home.
Gil Hoffman, a political analyst at the Jerusalem Post, told Al Jazeera that, while fragile, the ceasefire deal had the potential to make a lasting change.
"The practical effects of this [ceasefire] is that you are going to see a real effort on both sides to make lives better on both sides of the border," he said.
Hoffman said the ceasefire agreement would help Olmert amid an investigation that he allegedly accepted bribes before he became Israel's prime minister.
"This has come at a time when he is facing enough problems with criminal investigations. To have quiet in the Gaza Strip is something that would help him out tremendously."
Islamic Jihad, a Palestinian group which frequently fires rockets at Israel from Gaza, said it would observe the truce, despite having reservations about the deal.
"Despite our reservations over the truce agreement, we will not stand in its way and will not seek to cause its failure out of concern for Palestinian unity and in order to achieve the lifting of the blockade [on Gaza]," Nafez Azzam, a leader of the group, said on Wednesday.
"We did not sign any document but we gave our verbal agreement to Hamas and to Egypt while at the same time expressing our reservations."
Khalil al-Haya, a Hamas leader, speaking in Gaza on Tuesday, said that Egypt will seek to extend the truce into the West Bank.
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.