Prime Minister Ehud Olmert struggled behind closed doors to assert his authority on Tuesday after his diplomatic platform was rejected by both his successor as Kadima leader and Palestinian Authority President Mahmoud Abbas. At a rally in Ramallah, Abbas rejected Israeli concessions on Jerusalem and refugees, just one day after Olmert publicly stated he would come close to returning Israel to the pre-1967 borders in a final-status agreement. Abbas's words dealt yet another blow to Olmert, who was slammed for his views by Kadima politicians - including new party leader Tzipi Livni, who laid bare the chasm between them on the issue in an interview with Army Radio. Although Attorney-General Menaham Mazuz has ruled that Olmert has the legal authority to continue negotiations with the Palestinians as head of a lame duck government, and Olmert still insists in private conversations that it is he and he alone who leads the Palestinian negotiations, Livni declared Olmert had become irrelevant to those talks. Defiantly, an Olmert source told The Jerusalem Post that it was the prime minister's negotiations with the Palestinians that mattered, not Livni's. Neither the source not the Prime Minister's Office addressed the issue of Abbas's statements. "We rejected Israeli proposals that stipulated making concessions, including on Jerusalem and the refugees," Abbas said in Ramallah, according to DPA. "We either get all six points - Jerusalem, settlements, borders, refugees, water and security - or nothing at all," he said. A Livni spokesman was quick to say Abbas's statements were evidence of Livni's prominence over Olmert. Abbas, the spokesman said, was referring to an offer made by Olmert, and not to the series of talks between the foreign minister and former PA Prime Minister Ahmed Qurei. Fresh from Sunday's show of international support at Sharm e-Sheikh for the bilateral talks she has led with the Palestinians, Livni attacked Olmert on Army Radio for his speech at the official ceremony for Yitzhak Rabin on Monday. "As the head of the Kadima party, I am obligated not to the parting words of Olmert, but to Kadima's platform, which I wrote and in which I believe," Livni said. It was that platform alone, she said, "which determines the principles by which I negotiate." Livni said Olmert's speech reflected neither her views nor those of the Kadima party. Army Radio quizzed her as to whether she would tell the Palestinians and or the Americans that Olmert's statement was irrelevant. "There are things that you do not have to say. I am leading the negotiations," Livni said. However, a source close to Olmert told the Post that the prime minister would decide how the negotiations would progress until he left office after the national elections in February and the formation of a new government. At Sunday's meeting of Kadima ministers, the source said, Olmert made a point of saying that in the United States, President-elect Barack Obama had said that until he took office on January 20, outgoing President George W. Bush was still in charge. Olmert, according to the source, said Livni should extend the same courtesy to him. On Monday, the prime minister made waves in his party when he went well beyond its platform by saying: "We must relinquish Arab neighborhoods in Jerusalem, and return to that territory which comprised the State of Israel until 1967, with the necessary adjustments stemming from the realities created on the ground." It was one of the more succinct public summations of Olmert's stance to date. And it was condemned by politicians from the Right and from within Kadima. "It was a very great error," said MK Marina Solodkin (Kadima). "It was silly and very dangerous." Although within Israel, Olmert no longer carries the political weight of a prime minister, Solodkin said, in the eyes of the international community and the Palestinians he remains the country's leader. As such, when he spoke, the outside world believed he still represents Israel. What scares Solodkin, she said, is that despite the party's rejection of his statement, Olmert still has the legal authority to negotiate along those lines, even if doing so "betrays" the party's platform. Kadima was created to represent the center-Right and not the Left, Solodkin said. She did not support concessions on Jerusalem, and neither did the party's platform, she added. On the other hand, as Education Minister and Peace Now co-founder Yuli Tamir (Labor) sat at Mount Herzl Cemetery on Monday and listened to Olmert, one word crossed her mind: "Finally." Despite all the denials from Kadima politicians, Tamir said she was certain Olmert's words represented their views. "I am sure that when Tzipi Livni sits with Abu Ala [Ahmed Qurei]," there are not that many options, Tamir said. The most likely scenario is that the Etzion Bloc, the Ariel Bloc and the Jewish neighborhoods in east Jerusalem will be included within Israel's final borders, in exchange for territory from within the Green Line, she said. But even as she felt a sense of relief at Olmert's words, Tamir also was frustrated that he had made his position public only months before left office. It happened that way with former prime minister Ariel Sharon as well, she said. "Everyone who finishes a term [as prime minister] realizes that this is the only point of view," Tamir said. Given the assumption that Binyamin Netanyahu would become the next prime minister, after the Rabin memorial ceremony, Tamir told the Likud leader, "You are the only one who we have to convince, because all the rest are on our side." Netanyahu has said he plans to talk with the Palestinians, but not according to the principles set by Livni. In her radio interview, Livni said that in the end it was the February 10 elections that would determine Israel's negotiating stance with the Palestinians. The voters would decide whether she or Netanyahu would replace Olmert as prime minister, Livni said. "The rest of what will be said in the next few months will be less relevant," she said. However, Livni said, the final-status agreement would require territorial concessions by Israel. But these would be done in a way that preserves the Jewish state's security, takes account of places of historical significance such as Jerusalem, and allows the maximum number of settlers to remain in their homes, Livni said. As for Palestinian refugees, they would not be allowed to come to Israel. To reach a final-status agreement, she said, "there are things that we have to accept. There are things that if we do not accept, there won't be an agreement. That is part of the negotiations," she said. Just on Sunday, Livni continued, her role as the public face for these talks was affirmed by the international community, at the Quartet meeting at Sharm e-Sheikh. In that gathering, the Quartet agreed with her request to continue the bilateral nature of the negotiations with the Palestinians, in which neither side would be pressured to give up its interests, she said. It also agreed that no other initiative would be introduced. These talks must address all core issues to conclude the final-status agreement, Livni said. "Until everything is done, nothing is done." The Quartet's statement of support for those talks based on her principles, Livni said, showed "you can negotiate together with the Palestinians and with the world's approval, without getting to the points that Olmert said yesterday." Gil Hoffman contributed to this report.