At the time, Olmert said Hamas' demands were excessive and indicated he would turn the matter over to his successor, Benjamin Netanyahu, who is expected to be sworn in as the new prime minister within two weeks.
At a ceremony marking Schalit's 1,000th day in captivity on Saturday, the soldier's father, Noam, implored Olmert to use his remaining time in office to pursue his son's release.
Olmert spokesman Mark Regev said the government was trying to reach a deal with Hamas.
"The government of Israel is committed to achieving the release of Gilad Schalit. The work is ongoing," he said. He provided no further details.
The head of Hamas' government in the Gaza Strip, Ismail Haniyeh, also indicated a deal was still possible in an article published Sunday in Hamas' Al-Ray newspaper.
Haniyeh blamed Israel for the breakdown in talks, but wrote, "Our people are still trying to renew the Egyptian-sponsored negotiations in order to reach a respectable prisoner exchange that can include the prisoners concerned."
Israel agreed to release hundreds of Hamas prisoners but balked at releasing some of the masterminds of suicide bombings that killed dozens of Israeli civilians.
Speaking before his Cabinet's weekly meeting Sunday, Olmert said Israelis were still threatened by Palestinian attacks. Israeli police said a car bombing was thwarted late Saturday when the explosives-laden vehicle was discovered before it was able to blow up in the parking lot of a crowded mall in the northern city of Haifa.
Olmert said preliminary information showed the Haifa car bomb was dispatched by "a serious terror infrastructure that worked in sophisticated ways to carry out a terror attack with mass casualties."
Police spokesman Micky Rosenfeld said the powerful bomb contained hundreds of ball bearings meant to spray out on impact.
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