Demonstrators handed out yellow ribbons and hoisted banners demanding the release of the soldier, who was seized by Gaza militants in a June 2006 cross-border raid.
For nearly three years, Schalit's parents have been waging a campaign to bring their son home. Olmert, who had taken office just months before Schalit was captured, will step aside within weeks after a new government is installed.
"We demand that this government wrap this up once and for all and bring Gilad home," said Noam Schalit, the serviceman's father, who arrived at the protest tent on Sunday from the family's home in northern Israel. "We aren't telling the government how to do it. We are asking that Gilad be brought home."
"We will be here until this government ends its tenure and a new government is formed," said Aviva Schalit, the soldier's mother. Afterward, "we'll go back home and start counting the days again," she said.
Sunday marked Gilad Schalit's 987th day in captivity.
Fifty feet (15 meters) away, three fathers who lost children in a 2003 bus bombing urged the government not to give in to Hamas' demands that Israel free Palestinian prisoners involved in deadly attacks in return for Schalit.
"I'm in favor of releasing Gilad Schalit. I oppose releasing terrorists," said Ron Kehrmann, whose 17-year-old daughter died in the bombing in the northern city of Haifa.
Government spokesman David Baker had no comment on the Schalits' protest.
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