But critics have argued that the money is a fraction of the almost $600 million frozen since March when the Hamas-led government came to power.
In the meeting, Olmert pledged to release $100 million in tax rebates to the Palestinians and ease travel restrictions in the West Bank.
Saeb Erekat, a Palestinian negotiator, was upbeat about the talks. "This $100 million which is Palestinian money, will be spent in accordance with the appropriate channels and with the right co-ordination of all those concerned," he said.
However, the meeting between the Palestinian president and Olmert, and the agreed tax rebate, has been viewed with scepticism by some.
"Terrorism … they [Hamas] see it as a way of life"
Miri Eisen, Israeli government spokeswoman
Usamah Hamdan, a senior Hamas official, told Al Jazeera that Israeli's rebate was little more than a small step in the right direction, and that Hamas still had the support of the Palestinian people.
"I believe bringing in one-fifth of the money is not so good. It's a step in the right direction but it's not enough.
"I believe that support to Abu Mazen [Abbas] means we are still on track, regardless of how it was paid or to whom."
|Haniya has rejected election calls|
However, the meeting further served to delegitimise the role of Hamas as a democratically elected party of government.
Hamdan said: "Olmert wants to show the Israelis he has a friend on the Palestinian side. He wants to say to the international community that he is supporting Abu Mazen, but he is not giving him anything.
"If you want to talk about peace, then you have to talk about the side who is still committed to its people, its rights and who can apply all the agreements which it is supposed to accept.
"I believe Hamas is the only side which shows this," he said.
"There was a ceasefire until 2005, and even the Israelis said that the party really committed to this was Hamas," said Hamdan.
In praise of Abbas
However, Miri Eisen, an Israeli government spokeswoman, said that Hamas is an elected government that refuses to combine with the international community's principles and, therefore, Israel has no choice but to choose Abbas.
"Terrorism ... they [Hamas] see it as a way of life," she said.
"Olmert is reaching out. Where are the Palestinians within the Hamas-led government who say otherwise? President Abbas has spoken clearly. He talks about dialogue. He talks about moderation.
"He hasn't stopped with his vision of a Palestinian state alongside Israel. But he says, let's achieve it through dialogue and not through violence."
Israeli commitment questioned
During the meeting, no agreement was reached on the release of an Israeli soldier captured in a cross-border raid in July, nor on the release of the hundreds of Palestinian prisoners held by Israel.
"Hamas is representing the Palestinian people and they respect the decisions being made by Hamas"
Ghazi Hamed, a senior Hamas spokesman, said: "Until now, there has been no serious decision taken by the Israeli government to show that they are serious about facilitating the life of the Palestinian people."
The meeting came less than two months after 20 Palestinians were killed and 40 injured in Beit Hanoun when the Israeli army shelled the town a day after pulling its forces back from northern Gaza.
"Hamas is representing the Palestinian people and they respect the decisions being made by Hamas," said Hamdan.
"But the blood of the people is still warm from Beit Hanoun."