Olmert made the remarks Monday at a meeting of the Foreign Affairs and Defense Committee, a New York Times correspondent reported from Jerusalem.
"I'm not sure we can reach an agreement, and I'm not sure we can reach its implementation," Olmert said, adding he would be "committing a sin to my duty" if he didn't try.
During a visit last Thursday, Bush said he believed the two sides could have a deal signed to create a Palestinian state by the time he leaves office next January.
Livni said there was no place for the media in the talks.
"Faced with a choice between headlines and daily drama as opposed to results, I choose results," Livni said.