Barnaby Phillips, reporting for Al Jazeera from Jerusalem, said while Rice had said she was prepared to give the unity government a chance, the US and Israel were united on the "broad issues."
He said: "That is leading to a deep sense of pessimism on the Palestinian side."
Olmert told the weekly Israeli cabinet meeting: "I spoke about this on Friday with the president of the United States, and I can tell you the Israeli and US positions are completely identical."
He said in broadcast remarks: "A Palestinian government that does not accept the Quartet's conditions cannot receive recognition and there will not be co-operation with it."
International mediators have called for the new Palestinian unity government, agreed between Abbas and representatives from the ruling Hamas party, to recognise Israel, renounce violence and abide by interim peace accords.
The unity deal that Abbas and Hamas leaders reached in Saudi Arabia this month fell short of meeting the conditions set by the Quartet, a group comprised of the US, the European Union, Russia and the UN.
Ismail Haniya, the Palestinian prime minister and senior Hamas leader, has consistently refused to accept the status of Israel.
Rice had earlier been asked whether there was agreement to boycott a unity government.
She did not respond, although she said on Saturday such a decision had not yet been made.
"We are not going to render judgment [on a future unity government]," Rice's spokesman, Sean McCormack, said.
Nour Odeh, Al Jazeera's correspondent in Gaza, said ordinary Palestinians remain pessimistic of tangible results from the tripartite talks.
"It seems ordinary Palestinians aren't buying into the hopes being marketed by this trilateral summit," said Odeh.
"[Palestinians have] seen other summits come and go in the past without getting any closer to realising their aspirations"
Nour Odeh, Al Jazeera's Gaza correspondent
"They've seen other summits come and go in the past without getting any closer to realising their aspirations ... . The sceptical outlook about the summit among Palestinians from all walks of life reflects their conviction that American foreign policy is aligned with the Israeli occupation."
While publicly supportive of Abbas, US officials are becoming impatient with the Palestinian president, whose staff said he would not budge from the deal struck with Hamas.
More than 90 Palestinians have been killed in recent factional warfare between Fatah and Hamas, and the unity agreement has put a check on violence between the two groups.
Both groups hope the unity deal can put a permanent end to internal violence and also persuade Western donors to restore direct aid to the Palestinian Authority that was cut off after Hamas came to power.