Palestinian militants have fired rockets into Israel, hours after an unexpected ceasefire was called between the two sides.
Israel says it has pulled all its forces out of Gaza
At least three rockets were fired, one of which landed in the town of Sderot, without causing injury or damage.
Israeli PM Ehud Olmert said Israel will exercise "patience and restraint".
The ceasefire came into effect at 0600 (0400 GMT) after the Palestinian Authority said groups would end attacks and Israel agreed to halt hostilities.
The United States welcomed the ceasefire, calling it a "positive step forward".
Speaking hours after the rocket fire, Mr Olmert said Israel has "the strength to show the patience and restraint to allow the ceasefire to take hold.
"I have personally told our security forces to show restraint," he added
Israel's Defence Minister Amir Peretz however warned that Israel would resume its military operations in Gaza if the rockets did not stop.
Hamas' armed wing said it launched the attacks because some Israeli troops were still in Gaza, east of the town of Jabaliya, despite the Israelis saying they had pulled out all their troops overnight.
A statement from the smaller Islamic Jihad group said it would not agree to a ceasefire while Israeli military activity continued in the occupied West Bank.
The BBC's Alan Johnston in Gaza says the ceasefire violations have been condemned by a Hamas government spokesman and it is understood that efforts are being made within both Hamas and Islamic Jihad to bring the situation under control and make the truce work.
Palestinian Authority President Mahmoud Abbas meanwhile has ordered his security forces to deploy across northern Gaza and enforce the ceasefire, Palestinian security sources said.
Mr Abbas telephoned Mr Olmert on Saturday night to say he had agreement from all Palestinian factions that they would stop their rocket fire.
Mr Olmert's spokeswoman Miri Eisin told the BBC that the prime minister had agreed that Israeli forces would not initiate any offensive action after the ceasefire began.
Shortly after the truce came into effect, the Israeli army confirmed that all its troops had left Gaza.
Israel evacuated its settlements and military bases in Gaza last year after 38 years in the territory, but the military renewed ground operations after militants captured an Israeli soldier, Cpl Gilad Shalit, in a border raid in June.