Hundreds of people joined the protests in Jerusalem
The head of Israel's security services is in Cairo for talks aimed at securing the release of a captured Israeli soldier, Gilad Shalit.
Sgt Shalit has been held in Gaza since being kidnapped by Palestinian Hamas militants in 2006.
Hundreds of Israelis gathered in Jerusalem on Friday calling on the government to agree a prisoner swap deal with Sgt Shalit's captors.
The Israeli government is expected to discuss a deal on Monday.
Egypt has been mediating the discussions between Israel and Hamas.
Israel's outgoing Prime Minister Ehud Olmert said Shin Bet chief Yuval Diskin and veteran negotiator Ofer Dekel would return from Cairo on Sunday and report to the cabinet the next day.
"The government will receive the update and in accordance with the circumstances and the information, we will decide which decision should be made," Mr Olmert said in a statement.
Interior Minister Meir Sheetrit said the talks in Cairo would decide the issue "for better or worse".
He said great efforts had been made to reach a deal over the weekend, and Hamas understood that "the days of this government are numbered".
"This government is ready to approve a deal, but if the government is replaced, there is no telling what will be," said Mr Sheetrit.
Mr Olmert had made the release of Sgt Shalit a major issue of his premiership - but has only weeks left in office.
Sgt Shalit's family and supporters have said they fear a more harder-line cabinet led by Prime Minister-designate Benjamin Netanyahu might be less likely to do a deal.
Nothing has been heard from Sgt Shalit since 2008
On Friday, protesters joined Sgt Shalit's parents, who are staying in a tent near the house of outgoing PM Ehud Olmert.
At one stage, crowds of protesters blocked the road leading to Mr Olmert's residence, chanting: "Olmert, you made a promise, Olmert, keep it."
Sgt Shalit's father, Noam, told Israeli media he was encouraged by the show of support.
"We only organised the place, not the people. They came from all over the country spontaneously," he told the website of the Yediot Aharonot newspaper.
The Shalits set up a tent in front of Mr Olmert's house last Sunday, escalating their campaign after the prime minister said demonstrations calling for Sgt Shalit's release were unhelpful.
Gilad Shalit was seized in June 2006 by Palestinian militants, including members of the Hamas group which runs Gaza, in a raid into Israel that also left two Israeli soldiers dead.
Egypt has been brokering talks to secure his release. Hamas are demanding the release of more than 400 of the thousands of Palestinian prisoners held by Israel.
Nothing has been heard from the Israeli conscript since June 2008, when a letter in his handwriting was delivered to the Carter Centre in Ramallah in the West Bank.