The US, Israeli and Palestinian leaders have voiced hope that a conference in Maryland could produce a starting point for serious peace negotiations.
Speaking at a dinner for participants, US President George W Bush expressed his "personal commitment" towards resolving the conflict.
But he warned "difficult compromises" lay ahead for both sides.
Correspondents say expectations for Tuesday's meeting in the city of Annapolis are modest.
More than 40 organisations and countries, including Saudi Arabia and Syria, are attending the conference at a US naval academy.
The US Secretary of State, Condoleezza Rice, has been meeting Israeli and Palestinian teams in an effort to clinch a joint statement that sets out an outline for how negotiations will proceed post-Annapolis.
'This time it's different'
Mr Olmert and Mr Abbas had separate meetings with Mr Bush in the White House on Monday.
Mr Olmert told reporters the "international support" provided by participants was a crucial factor in his optimism.
"This time it's different because we are going to have lots of participants in what I hope will launch a serious process of negotiations between us and the Palestinians," Mr Olmert said.
But Mr Olmert also cautioned that no peace deal could be agreed without the halting of rocket attacks into Israel from Gaza - controlled by the Islamist movement Hamas, which has stayed away from the conference.
For his part, Mr Abbas praised the initiative but said talks would have to address the thorny obstacles to Palestinian statehood - the "permanent-status issues" - that have felled previous attempts at peace negotiations.
Israeli settlers voiced their opposition to the talks
"We have a great deal of hope that this conference will produce... expanded negotiations over all permanent-status issues that would lead to a peace agreement between Israel and the Palestinian people," he said after meeting Mr Bush.
"This is a great initiative and we need his [Mr Bush's] continuing effort to achieve this objective."
Mr Bush also earlier said he was also "optimistic" for the prospects for a serious dialogue.
Later, at the formal dinner for all the participants in Washington, he said both sides shared a "common goal: two democratic states, Israel and Palestine, living side by side in peace and security".
Nevertheless, given the history of failed attempts at peace negotiations correspondents are not ambitious about what can be achieved at this meeting.
There is no readiness at the moment to agree a deal, says the BBC's Justin Webb in Washington.
The talks simply seek to assure both sides that the United States and the big Arab powers will do what is necessary to support a dialogue, and to get a firm commitment to the launch of that dialogue, he says.
High-level officials in Washington have expressed scepticism about the talks.
In Jerusalem, at least 10,000 Israeli settlers protested against the talks, some bearing placards reading "Don't feed Israel to the sharks".
And Hamas, which controls the Gaza Strip, has repeated its assertion that any decision taken at Annapolis would not be binding on the Palestinian people.
"[They] have not authorised anyone, either Arab or Palestinian, to erase their rights," Hamas spokesman Fawzi Barhum told AFP news agency.
Hamas won a landslide victory in the January 2006 legislative election but is designated a terrorist organisation by the US, the EU and Israel.
The government has been subject to economic and diplomatic sanctions by Israel and its allies in the West.