The Israeli cabinet has approved the release of $100m (£51m) in frozen Palestinian funds.
Mr Abbas was introduced to Mr Olmert's wife, Aliza
The move was agreed at the first meeting between Prime Minister Ehud Olmert and Palestinian Authority (PA) President Mahmoud Abbas.
Israel has withheld $600m in tax revenues from the PA since Hamas formed a government earlier this year.
It says it will hand over the funds for humanitarian purposes if a mechanism can be found to bypass Hamas.
The two leaders also agreed to establish or re-establish three joint committees - a security committee to discuss the expansion of the current shaky Israeli-Palestinian ceasefire in Gaza to include the West Bank; a financial committee tasked with the transfer of tax revenues and other funds to the PA; and another to deal with eventual prisoner exchanges.
But the BBC's Katya Adler in Jerusalem says many Israelis and Palestinians remain sceptical - agreements are one thing, their implementation quite another.
The meeting, at Mr Olmert's residence in the city, lasted nearly two hours.
The pair met informally in June, but these were the first formal talks between Israeli and Palestinian leaders for nearly two years.
Mr Abbas was greeted by the Israeli leader as he arrived for the meeting. The two men shook hands and kissed each other on the cheek, then Mr Olmert introduced his guest to his wife Aliza before they sat down to talk.
"This is the beginning of a series of meetings. It was a good meeting. There was agreement on several issues," Palestinian official Nabil Abu Rdainah told Reuters news agency.
Civil war fears
Mr Abbas and Mr Olmert have both said recently that they want to re-start peace talks, but both sides have also played down the prospects for any rapid progress.
Israel has repeatedly said it will not deal with the Hamas-led Palestinian government, which refuses to recognise the legitimacy of the Jewish state. Mr Abbas says his attempts to persuade Hamas to change its position have failed.
Last week he called for early elections, but Hamas denounced this as a coup attempt.
The dispute led to some of the worst factional fighting between Palestinians in years, prompting fears that the violence was descending into all-out civil war.
Israel has been under pressure from the US and the European Union in recent days to take steps to support Mr Abbas, our correspondent says.
Correspondents say a breakthrough in the stalled Middle East peace process would help both leaders, with Mr Abbas suffering from the conflict with Hamas, and Mr Olmert losing popularity in Israel over his handling of the war with Lebanon this summer.