"A Palestinian government that does not accept the Quartet's conditions cannot receive recognition and there will not be co-operation with it," Olmert said in broadcast remarks.
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.
"A Palestinian government that does not accept the Quartet's conditions, cannot receive recognition and there will not be cooperation with it," Olmert said in broadcast remarks.
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 United States, the European Union, Russia and the United Nations.
Hamas, led by Ismail Haniyeh, the Palestinian prime minister, 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," said Odeh.
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.