Mr. Olmert was speaking on Sunday as the ceasefire went into effect.
Under the agreement, Palestinian militant groups were to stop all rocket fire, with Israel to withdraw its forces from the Gaza Strip.
Mr. Olmert said he ordered the Israeli army to show restraint following Palestinian rocket attacks to give the ceasefire a chance to take hold.
The armed wing of Islamic Jihad and the ruling Islamist movement, Hamas, took responsibility for Sunday's attacks.
To bolster the ceasefire, Palestinian President Mahmoud Abbas deployed Palestinian security forces along the Gaza-Israel border.
The Israeli newspaper Jerusalem Post is reporting that two Palestinian militant groups have threatened to resume attacks on Israel if military operations continue in the occupied West Bank.
The newspaper quotes a spokesman Abu Obaidah of Hamas's armed wing as saying any Israeli assault in the West Bank will be viewed as a violation of the ceasefire agreement.
The newspaper says the al-Aksa Martyrs Brigades, linked to Mr. Abbas's Fatah faction, issued a similar threat.
Under the accord reached Saturday, Israel withdrew its forces from Gaza. Israel pulled its soldiers and settlers out of the Gaza Strip last year. But troops moved back into the area in June when Palestinian militants captured an Israeli soldier in a cross-border raid.
Information for this report is provided by Reuters and AFP