The Gaza Strip has been a focus for recent violence
The Palestinian Islamist movement, Hamas, has proposed a six-month "period of quiet" in Gaza, which it says could then be extended to the West Bank.
Former Palestinian foreign minister Mahmoud Zahhar said the truce would have to be mutual and include the lifting of an Israeli blockade of Gaza.
But an Israeli government spokesman dismissed the proposal as a ruse to allow Hamas to "re-arm and re-group".
Meanwhile, two Israeli security guards have been shot dead in the West Bank.
The Israeli military said the men were screening workers at the Nitzanei Shalom industrial zone, near the northern town of Tulkarm, when a Palestinian militant approached them, opened fire at close range and then fled.
The industrial zone, which contains five Israeli-owned factories that employ local Palestinians, is located on the Palestinian side of the West Bank barrier.
The Israeli government condemned the shooting as a "clear example of extremism and terrorism by those seeking to foil any prospects for advancing peace".
Hamas and the Islamic Jihad militant group said they had carried out the attack jointly. An Islamic Jihad spokesman told the Associated Press the gunman had been lightly wounded.
UN aid deliveries halted
Mr Zahhar, a senior Hamas leader in Gaza, announced his group's proposal for a conditional truce at talks with Egyptian intelligence chief Omar Suleiman in Cairo. Mr Suleiman has been the main point of contact between Hamas and Israel.
"The truce must be mutual and simultaneous and the blockade must be lifted and the crossing points opened," Mr Zahhar said, adding that this included the Rafah crossing between Gaza and Egypt.
Rafah has mostly been closed since Hamas seized control of the Gaza Strip in June, though Palestinian militants temporarily breached the crossing earlier this year, allowing hundreds of thousands of Gazans to buy food and other essentials.
Mr Zahhar said the truce "could be expanded to the West Bank and would be set at six months" and that Palestinian factions would be invited to discuss the proposal next week by the Egyptian mediators.
Hamas had previously said that a truce should begin at the same time in both Gaza and the West Bank.
Mr Zahhar added that it was now up to Israel whether or not to approve the ceasefire, saying "the ball is in the Israeli court". If Israel does not comply, "then it will be our right to defend our people in all legitimate ways", he warned.
Israel says it reserves the right to protect its citizens by military action
The Israeli government, however, dismissed the offer.
"Hamas is biding time in order to re-arm and re-group," Israeli government spokesman David Baker told the Reuters news agency.
"There would be no need for Israel's defensive actions if Hamas would cease and desist from committing terrorist attacks on Israelis."
Gaza has been a focus of recent violence, with the Israeli military carrying out raids to target Hamas members, while Hamas has fired rockets at nearby Israeli towns.
Israel has all but sealed off the Gaza Strip since Hamas took control of the area.
On Thursday, the UN said that it had halted humanitarian assistance operations in Gaza because it had run out of fuel for its vehicles.
Israeli sanctions imposed in an attempt to curtail rocket fired by Palestinian group Hamas have caused shortages, but Israel says Hamas is preventing fuel distribution.
More than 80% of Gaza's population relies on aid, with UN food hand-outs going to about 1.1 million people - many them children.