"But then in the Middle East if you wait for the perfect circumstances you would probably never take the airplane," Rice said in an interview with US newspaper reporters.
The talks had been billed as the start of a renewed US effort to try to broker a Middle East peace deal, but Rice and others sought to lower expectations.
Some officials in Jerusalem have said the focus would be on US and Israeli concerns about the unity government deal.
"The purpose of the trilateral is just really to begin a conversation to look on how we can move forward on what everyone believes is the most important goal of two states living side by side," said Rice.
But Middle Eastern diplomats and analysts pointed to the weakness of both Olmert and Mahmoud Abbas, the leader of Fatah and the Palestinian president, as well as changes in the president's tactics by forging a deal with Hamas.
"Palestinians must focus on the end objective and not get sidetracked by destructive actions"
The Bush administration is deliberating on how to handle contacts with a new Palestinian government that includes both
Hamas and Fatah.
A Palestinian official said Abbas was told that Washington would boycott all members unless international demands on policy towards Israel were met.
But Rice, who declined to discuss diplomatic conversations with the Palestinians, said Washington was holding back on making any judgments until details of a new government were known.
"We are not going to jump the gun here," she said. But Rice made clear that the US fully supported Abbas and his peace efforts with Israel.
"It would be a very big mistake to not continue to deal with him and to not continue to build on his commitment to a two-state solution and to non-violence," she said.
The US goal of bolstering Abbas and isolating Hamas has also hit a snag in congress, where a US lawmaker is blocking a request by the Bush administration for $86m to help train Abbas's security forces.
"The strategy of strengthening Abu Mazen [Abbas] over Hamas has been pre-empted and that changes both what the US was trying to do and how the US was trying to do it," said Middle East expert Jon Alterman.
Ned Walker, the former US ambassador to Israel and Egypt, said it was unrealistic to expect any breakthroughs from next week's three-way meeting in Jerusalem.
"It seems to me that it is good to do this, but we should not put too much of a high expectation on this and undercut the secretary and her efforts," said Walker.