"There is nothing that encourages us to continue with a deal that did not achieve the results we hoped for."
Mark Regev, spokesman for the Israeli prime minister, Ehud Olmert, told news agency AP that Israel was committed to the truce but "it's clear there can't be a one-sided ceasefire".
"Israel cannot unilaterally accept a situation where rockets are everyday coming from the Gaza Strip targeting Israeli civilians," he said.
There have been sporadic violent clashes along the Israeli-Gaza border in the past two months, with both sides accusing each other of violating the truce.
"There is no legitimacy to the extension of Abbas's presidency after January 9"
Ismail Haniya, Hamas leader in the Gaza Strip
Israeli troops have carried out raids within the Strip while Hamas fighters have launched rocket attacks on southern Israel.
Israel has since stepped up its blockade of Gaza, which has attracted widespread international criticism, until, it says, Hamas puts an end to rocket attacks.
The latest development came as Ismail Haniya, the Hamas leader in the Strip, addressed thousands of people gathered on Sunday in Gaza's main square to celebrate the 21st anniversary of Hamas.
"The first priority for us in Hamas is national dialogue and the lifting of the siege. We call upon the Arab and Muslim communities to lift the siege on Gaza," he said.
Haniya also criticised moves to extend the presidency of Mahmoud Abbas, the chair of Fatah and president of the Palestinian Authority, beyond January 9, 2009.
"There is no legitimacy to the extension of Abbas's presidency after January 9 ... we don't understand the declaration of Abbas as the president of the state of Palestine. Which state are they talking about?" he said.
Fatah immediately hit back a Haniya's remarks, calling them "miserable" and indicative of "the insolence of Hamas".
"Haniya's statement on the term of the president is worthless," said Fahmi Al-Zaarir, Fatah's spokesman in the West Bank. He added that Fatah was ready to hold presidential and parlimentary elections "immediately".
Ayman Mohyeldin, Al Jazeera's correspondent in Gaza, said Gazans are highly sceptical about the ceasefire.
"They say, so far, the existing truce has not brought any gains to the people in Gaza. People say the ongoing siege is a stark example of how Israel has treated Gazans," he said.
Officials from Israel and Egypt, which has acted as a mediator between the two sides, are expected to meet in Cairo on Sunday to discuss extending the ceasefire.
Meanwhile, the United Nations is expected to pass a resolution calling for peace in the Middle East for the first time in five years.
The Security Council will meet on Tuesday to discuss a US-sponsored resolution, which calls for peace efforts between Israel and the Palestinians to be intensified.