Olmert has made freedom for Gilad Shalit, an Israeli soldier held by Palestinian fighters in the Gaza Strip since 2006, a pre-condition for a wider truce with Hamas.
Shalit, now 22, was captured by fighters who tunnelled into Israel from the Gaza Strip and took him into the Hamas-ruled territory.
Conditions for release
The reopening of the Gaza borders to reconstruction aid - following Israel's offensive in December and January - is also a condition for Shalit's release.
In exchange for Shalit, Hamas has demanded the release of 1,400 Palestinian prisoners, including about 450 long-serving inmates.
Some of those were convicted of attacks that killed Israelis, and critics say a large prisoner swap for Shalit could encourage Hamas and others to try to seize more soldiers.
"We reject expulsion. There is no room for more flexibility in our position"
Abu Ubaida, spokesman of the Hamas armed wing
"There is progress and there is a new (Israeli) proposal, but there are still some differences blocking conclusion of a deal," a senior Hamas official said.
Al Jazeera's Mike Hanna, reporting from Jerusalem, said Hamas has been "consistent in its demands in terms of negotiations that have been ungoing for a long period of time".
It was only last month that "Israel attached the question of the release of Gilad Shalit to the wider negotiations concerning a lasting ceasefire in Gaza", he said.
"So, in a way, Israel changed the terms of the debates about both the release of Shalit and in terms of the question of creating a ceasefire in Gaza and ending that ongoing Israeli blockade.
"From Israel's point of view, it says that Hamas came up with new demands that it regarded as unacceptable. Hamas said it was standing by the demands it had been making over a period of time. Each side [is] attempting to put some form of spin on the situation."
Issue of exile
Another dispute centred on Israeli demands that some of the prisoners be exiled.
"We reject expulsion," Abu Ubaida, a spokesman of Hamas's armed wing, Izz el-Deen al-Qassam Brigades, said on Sunday.
"There is no room for more flexibility in our position."
|Israel has made the release of Shalit a pre-condition for a wider truce with Hamas EPA]
Olmert had scheduled a cabinet meeting for Monday, but moved it to Tuesday to give his envoys, Yuval Diskin, head of the Shin Bet security service, and negotiator Ofer Dekel more time to try to seal a deal.
"The ministers will be briefed on the negotiations," Mark Regev, the spokesman for Olmert, said.
"If there is a need to take decisions, decisions can be taken."
Israeli media said earlier that the cabinet might decide on Tuesday to send the envoys back to Cairo for more talks.
Hamas was represented in the talks for the first time by Ahmed al-Jaabari, a senior commander.
Olmert is in the final days of a three-year term marked by a 2006 Lebanon war that many Israelis see as a failure and a 22-day Gaza campaign that ended in January without achieving a complete halt to cross-border rocket fire.
"Olmert will brief his outgoing government on the state of the affairs ... There is likely to be a semi-formal handover of the entire matter to the incoming government - one that would be led by Binyamin Netanyahu," our correspondent said.
"At this stage we do not know what the nature of that government is going to be. All indications are that it will be a narrow right-wing coalition government including parties to the extreme right of Israeli politics."
Members of Olmert's outgoing administration have warned Hamas publicly that it may find a new hawkish government being formed by Benjamin Netanyahu less willing to deal on prisoners.
Israel has carried out lopsided exchanges in the past, trading large numbers of Arab prisoners for its captured soldiers or their remains.